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Опубліковано: 14 березня 2023

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Статті в журналах з теми "Focusing Nonlinear schroedinger equation"

Kamvissis, Spyridon. "Long time behavior for the focusing nonlinear schroedinger equation with real spectral singularities." Communications in Mathematical Physics 180, no. 2 (October 1996): 325–41. http://dx.doi.org/10.1007/bf02099716.

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Benci, Vieri, Marco Ghimenti, and Anna Maria Micheletti. "The nonlinear Schroedinger equation: Solitons dynamics." Journal of Differential Equations 249, no. 12 (December 2010): 3312–41. http://dx.doi.org/10.1016/j.jde.2010.09.026.

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ABLOWITZ, MARK J., and CONSTANCE M. SCHOBER. "HAMILTONIAN INTEGRATORS FOR THE NONLINEAR SCHROEDINGER EQUATION." International Journal of Modern Physics C 05, no. 02 (April 1994): 397–401. http://dx.doi.org/10.1142/s012918319400057x.

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Hamiltonian integration schemes for the Nonlinear Schroedinger Equation are examined. The efficiency with respect to accuracy and integration time of an integrable scheme, a standard conservative scheme, and a symplectic method is compared.

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Kim, Jong Uhn. "Invariant measures for a stochastic nonlinear Schroedinger equation." Indiana University Mathematics Journal 55, no. 2 (2006): 687–718. http://dx.doi.org/10.1512/iumj.2006.55.2701.

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Plastino, A. R., and C. Tsallis. "Nonlinear Schroedinger equation in the presence of uniform acceleration." Journal of Mathematical Physics 54, no. 4 (April 2013): 041505. http://dx.doi.org/10.1063/1.4798999.

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Degasperis, A., S. V. Manakov, and P. M. Santini. "Multiple-scale perturbation beyond the nonlinear Schroedinger equation. I." Physica D: Nonlinear Phenomena 100, no. 1-2 (January 1997): 187–211. http://dx.doi.org/10.1016/s0167-2789(96)00179-0.

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Jeanjean, Louis, and Kazunaga Tanaka. "A positive solution for a nonlinear Schroedinger equation on R^N." Indiana University Mathematics Journal 54, no. 2 (2005): 443–64. http://dx.doi.org/10.1512/iumj.2005.54.2502.

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Duell, Wolf-Patrick, and Guido Schneider. "Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model." Indiana University Mathematics Journal 55, no. 6 (2006): 1813–34. http://dx.doi.org/10.1512/iumj.2006.55.2824.

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Mel'nikov, V. K. "Integration of the nonlinear Schroedinger equation with a self-consistent source." Communications in Mathematical Physics 137, no. 2 (April 1991): 359–81. http://dx.doi.org/10.1007/bf02431884.

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Bountis, Tassos, and Fernando D. Nobre. "Travelling-wave and separated variable solutions of a nonlinear Schroedinger equation." Journal of Mathematical Physics 57, no. 8 (August 2016): 082106. http://dx.doi.org/10.1063/1.4960723.

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Дисертації з теми "Focusing Nonlinear schroedinger equation"

Ortoleva, Cecilia Maria. "Asymptotic properties of the dynamics near stationary solutions for some nonlinear Schrödinger équations." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00825627.

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Анотація:

The present thesis is devoted to the investigation of certain aspects of the large time behavior of the solutions of two nonlinear Schrödinger equations in dimension three in some suitable perturbative regimes. The first model consist in a Schrödinger equation with a concentrated nonlinearity obtained considering a {point} (or contact) interaction with strength $alpha$, which consists of a singular perturbation of the Laplacian described by a self adjoint operator $H_{alpha}$, and letting the strength $alpha$ depend on the wave function: $ifrac{du}{dt}= H_alpha u$, $alpha=alpha(u)$.It is well-known that the elements of the domain of a point interaction in three dimensions can be written as the sum of a regular function and a function that exhibits a singularity proportional to $|x - x_0|^{-1}$, where $x_0$is the location of the point interaction. If $q$ is the so-called charge of the domain element $u$, i.e. the coefficient of itssingular part, then, in order to introduce a nonlinearity, we let the strength $alpha$ depend on $u$ according to the law $alpha=-nu|q|^sigma$, with $nu > 0$. This characterizes the model as a focusing NLS with concentrated nonlinearity of power type. In particular, we study orbital and asymptotic stability of standing waves for such a model. We prove the existence of standing waves of the form $u (t)=e^{iomega t}Phi_{omega}$, which are orbitally stable in the range $sigma in (0,1)$, and orbitally unstable for $sigma geq 1.$ Moreover, we show that for $sigma in(0,frac{1}{sqrt 2}) cup left(frac{1}{sqrt{2}}, frac{sqrt{3} +1}{2sqrt{2}} right)$ every standing wave is asymptotically stable, in the following sense. Choosing an initial data close to the stationary state in the energy norm, and belonging to a natural weighted $L^p$ space which allows dispersive stimates, the following resolution holds: $u(t) =e^{iomega_{infty} t +il(t)} Phi_{omega_{infty}}+U_t*psi_{infty} +r_{infty}$, where $U_t$ is the free Schrödinger propagator,$omega_{infty} > 0$ and $psi_{infty}$, $r_{infty} inL^2(R^3)$ with $| r_{infty} |_{L^2} = O(t^{-p}) quadtextrm{as} ;; t right arrow +infty$, $p = frac{5}{4}$,$frac{1}{4}$ depending on $sigma in (0, 1/sqrt{2})$, $sigma in (1/sqrt{2}, 1)$, respectively, and finally $l(t)$ is a logarithmic increasing function that appears when $sigma in (frac{1}{sqrt{2}},sigma^*)$, for a certain $sigma^* in left(frac{1}{sqrt{2}}, frac{sqrt{3} +1}{2sqrt{2}} right]$. Notice that in the present model the admitted nonlinearities for which asymptotic stability of solitons is proved, are subcritical in the sense that it does not give rise to blow up, regardless of the chosen initial data. The second model is the energy critical focusing nonlinear Schrödinger equation $i frac{du}{dt}=-Delta u-|u|^4 u$. In this case we prove, for any $nu$ and $alpha_0$ sufficiently small, the existence of radial finite energy solutions of the form$u(t,x)=e^{ialpha(t)}lambda^{1/2}(t)W(lambda(t)x)+e^{iDeltat}zeta^*+o_{dot H^1} (1)$ as $tright arrow +infty$, where$alpha(t)=alpha_0ln t$, $lambda(t)=t^{nu}$,$W(x)=(1+frac13|x|^2)^{-1/2}$ is the ground state and $zeta^*$is arbitrarily small in $dot H^1$

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Coleman, James. "Blowup phenomena for the vector nonlinear Schroedinger equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ63694.pdf.

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Khan, K. B. "The nonlocal-nonlinear-Schroedinger-equation model of superfluid '4He." Thesis, University of Exeter, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267224.

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Dodson, Benjamin Taylor Michael Eugene. "Caustics and the indefinite signature Schroedinger equation linear and nonlinear /." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2009. http://dc.lib.unc.edu/u?/etd,2306.

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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2009.
Title from electronic title page (viewed Jun. 26, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.

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Schober, Constance Marie. "Numerical and analytical studies of the discrete nonlinear Schroedinger equation." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185595.

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Certain conservative discretizations of the Nonlinear Schroedinger (NLS) Equation can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in for the two unstable mode regime and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We undertake an analysis to determine the mechanism that causes the "chaotic" behavior to appear in this conservatively perturbed NLS equation. This analysis involves the construction of explicit formulas for the homoclinic orbit, a description of the relevant finite dimensional phase space and a Melnikov analysis for the various regimes studied.

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Cruz-Pacheco, Gustavo. "The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187238.

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This work consists of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are derived for the persistence of NLS solutions under the CGL perturbation. For the traveling wave solutions, these conditions are derived for a general nonlinearity and written explicitly as two equations for the two continuous parameters which determine the NLS traveling wave. It is shown using a Melnikov argument that in this case these two conditions are sufficient provided they satisfy a transversality condition. As a concrete example, the equations for the parameters are solved numerically in the important case of the CGL equation with a cubic nonlinearity. For the case of the CGL equation with a general power nonlinearity, it is proved that the NLS homoclinic orbits to rotating waves are destroyed by the CGL perturbation. Special attention is dedicated to the cubic case. For this nonlinearity, the NLS equation is a completely integrable Hamiltonian system and a much larger family of its solutions can be written explicitly. The necessary conditions for the persistence of the NLS isospectral manifold are written explicitly as a system of equations for the simple periodic eigenvalues. As an example, the conditions for an even genus two solution are written down as a system of three equations with three unknowns.

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Barran, Sunil Kumar. "Modulation of the harmonic soliton solutions for the defocusing nonlinear Schroedinger equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ40028.pdf.

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Witt, Andy [Verfasser]. "Inducing Predefined Nonlinear Rogue Waves on Basis of Breather Solutions : Using Analytical Solutions of the Nonlinear Schroedinger Equation / Andy Witt." Berlin : epubli, 2019. http://d-nb.info/1192098285/34.

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Mancin, Fabio. "Ultra short solutions of a higher order nonlinear Schroedinger equation stability and applicability in dispersion managed systems /." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970076428.

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Borghese, Michael, and Michael Borghese. "A Proof of the Soliton Resolution Conjecture for the Focusing Nonlinear Schrödinger Equation." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624578.

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Анотація:

We give a proof of the long-time asymptotic behavior of the focusing nonlinear Schrödinger equation for generic initial condition in which we have simple discrete spectral data and an absence of spectral singularities. The proof relies upon the theory of Riemann-Hilbert problems and the ∂ ̄ method for nonlinear steepest descent. To leading order, the solution will appear as a multi-soliton solution as t → ∞.

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Книги з теми "Focusing Nonlinear schroedinger equation"

Sulem, C. The nonlinear Schrödinger equation: Self-focusing and wave collapse. New York: Springer, 1999.

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Sulem, Catherine, and Pirre-Louis Sulem, eds. The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/b98958.

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Sulem, C. The nonlinear Schrödinger equation: Self-focusing and wave collapse. New York: Springer, 1999.

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Kamvissis, Spyridon. Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation. Princeton, N.J: Princeton University Press, 2003.

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Kamvissis, Spyridon. Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation. Princeton, N.J: Princeton University Press, 2003.

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Sulem, Catherine, and Pierre-Louis Sulem. Nonlinear Schroedinger Equations: Self-Focusing and Wave Collapse (Applied Mathematical Sciences/139). Springer, 1999.

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Sulem, Catherine. The Nonlinear Schrödinger Equation: Self-Focusing And Wave Collapse. Springer, 2013.

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Kamvissis, Spyridon, Peter D. Miller, and Kenneth D. T.-R. McLaughlin. Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154). Princeton University Press, 2003.

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Частини книг з теми "Focusing Nonlinear schroedinger equation"

Folli, Viola. "Nonlinear Schroedinger Equation." In Springer Theses, 9–20. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4513-1_2.

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Folli, Viola. "Disordered Nonlinear Schroedinger Equation." In Springer Theses, 29–39. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4513-1_4.

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Boyd, John P. "Nonlinear Wavepackets and Nonlinear Schroedinger Equation." In Dynamics of the Equatorial Ocean, 405–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55476-0_17.

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Folli, Viola. "Weakly Disordered Nonlinear Schroedinger Equation." In Springer Theses, 21–28. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4513-1_3.

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Boyd, John P. "Envelope Solitary Waves: Third Order Nonlinear Schroedinger Equation and the Klein-Gordon Equation." In Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics, 325–65. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5825-5_13.

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Angenent, S. B., and D. G. Aronson. "The focusing problem for the Eikonal equation." In Nonlinear Evolution Equations and Related Topics, 137–51. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7924-8_7.

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Shvets, V. F., N. E. Kosmatov, and B. J. LeMesurier. "On Collapsing Solutions of the Nonlinear Schroedinger Equation in Supercritical Case." In Singularities in Fluids, Plasmas and Optics, 317–21. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2022-7_24.

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Kenkre, V. M. "The Discrete Nonlinear Schroedinger Equation: Nonadiabatic Effects, Finite Temperature Consequences, and Experimental Manifestations." In Davydov’s Soliton Revisited, 519–20. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-9948-4_43.

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Yamane, Hideshi. "Soliton Resolution for the Focusing Integrable Discrete Nonlinear Schrödinger Equation." In Springer Proceedings in Mathematics & Statistics, 95–102. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99148-1_6.

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Malkin, Vladimir. "Singularity formation for nonlinear Schrödinger equation and self-focusing of laser beams." In CRM Proceedings and Lecture Notes, 183–98. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/crmp/012/15.

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Тези доповідей конференцій з теми "Focusing Nonlinear schroedinger equation"

Luther, G. G., C. J. McKinstrie, and A. L. Gaeta. "Transverse Modulational Instability of Counterpropagating Light Waves." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.stdopd205.

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The transverse modulational instability (TMI) of two counterpropagating light waves in finite Kerr media is modeled by a pair of coupled nonlinear Schroedinger equations. This model predicts that transverse modulations in the wave amplitudes can be either convectively or absolutely unstable, in both self-focusing and self-defocusing media. In general, both frequency- and wavenumber-shifted sideband modes can grow if the wave intensities are unequal.

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Silberberg, Y., J. S. Aitchison, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith. "Experimental Observation of Spatial Soliton Interactions." In Integrated Photonics Research. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/ipr.1990.pd7.

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Spatial optical solitons are self-trapped optical beams which propagate without changing their spatial shape because of the competing effects of diffraction and self-focusing in a nonlinear medium1. Self-trapped beams are known to be unstable in bulk media, and to lead to catastrophic self-focusing. They are stable, however, when diffraction is limited to one spatial dimension, such as in planar optical waveguides. The spatial soliton is described by the non;linear Schroedinger equation, and it is completely analogous to the temporal soliton in optical fibers. Spatial solitons have recently been reported in multimode CS2 waveguides2 and single mode glass waveguides3. The nonlinear contribution to the refractive index, essential for the observation of these solitons, can also give rise to interaction forces between pairs of solitons. These forces have been studied theoretically4 and have been experimentally observed in the temporal domain5. Here we report the first experimental observation of interaction between spatial solitons.

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Chavez-Cerda, S., M. A. Meneses-Nava, V. Sanchez-Villicana, and J. Sanchez-Mondragon. "Oscillating solutions of the multidimensional nonlinear Schroedinger equation." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/nlgw.1998.nsnps.p5.

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We show analytically that there can exist oscillating bound states of the multidimensional nonlinear Schroedinger equations with Kerr and saturable nonlinearity which are breather-like solutions. The solutions have a rare peculiarity, the oscillating behavior takes place between the widths, with the amplitude kept almost constant. We confirm numerically our results.

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Akhmediev, N. N., and A. Ankiewicz. "Does the Nonlinear Schroedinger Equation Correctly Describe Beam Propagation?" In Integrated Photonics Research. Washington, D.C.: OSA, 1993. http://dx.doi.org/10.1364/ipr.1993.imb14.

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Li, Zhonghao, Guosheng Zhou, and Dachun Su. "N-soliton solutions in the higher-order nonlinear Schroedinger equation." In Photonics China '98, edited by Shuisheng Jian, Franklin F. Tong, and Reinhard Maerz. SPIE, 1998. http://dx.doi.org/10.1117/12.318024.

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Zaslavsky, George M., and Vasily E. Tarasov. "Fractional Generalization of Ginzburg-Landau and Nonlinear Schroedinger Equations." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84266.

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The fractional generalization of the Ginzburg-Landau equation is derived from the variational Euler-Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some different forms of the fractional Ginzburg-Landau equation or nonlinear Schro¨dinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.

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de Sterke, C. Martijn. "Theory of modulational instability in periodic media with a Kerr nonlinearity." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/nlgw.1998.nsnps.p12.

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Modulational instability in periodic media with a Kerr nonlinearity is investigated using coupled mode theory. In the presence of anomalous dispersion, the standard nonlinear Schroedinger results are obtained at low powers, though at higher powers deviations from this well-known behavior occur. For normal dispersion an instability with a finite threshold is found. This instability has no equivalent in the nonlinear Schroedinger equation.

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Vallée, Réal, and Michel Piché. "Instabilities of a dispersive nonlinear all-fiber ring cavity." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/nlgwp.1991.tue5.

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Nonlinear optical cavities have been proposed for many applications such as bistability and optical switching. They have recently found an important application as the fast modulating element in coupled-cavity mode-locking. In this paper, we address the problem of the dynamical instabilities at the output of an all-fiber ring cavity synchronously pumped by a pulse train from a sync. pumped dye laser. Our analysis is based on a numerical simulation of the Nonlinear Schroedinger (NLS) equation and is primarily intended to explain recent experimental results1.

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Duyckaerts, Thomas, Svetlana Roudenko, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Criteria for Collapse in the Focusing Nonlinear Schrödinger Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636831.

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Potasek, M. J., and R. Tasgal. "Exact soliton solutions for femtosecond switching in a nonlinear directional coupler." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.thmm19.

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Optical information processing is being recognized for its importance over a wide range of use. The recent focus has been on all-optical switching because of its ultrafast response time. One device configuration of interest is the nonlinear directional coupler. Most descriptions of switching in these systems have involved the coupled nonlinear Schroedinger equation (NLS) that describes switching usually on a picosecond time scale.

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Звіти організацій з теми "Focusing Nonlinear schroedinger equation"

Pitts, Todd Alan, Mark Richard Laine, Jens Schwarz, Patrick K. Rambo, and David B. Karelitz. Derivation of an applied nonlinear Schroedinger equation. Office of Scientific and Technical Information (OSTI), January 2015. http://dx.doi.org/10.2172/1167671.

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