Relevant bibliographies by topics / Singular Schrodinger equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Singular Schrodinger equation'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Singular Schrodinger equation"

1

Troy, W. C. "New singular standing wave solutions of the nonlinear Schrodinger equation." Journal of Differential Equations 267, no. 2 (July 2019): 979–1000. http://dx.doi.org/10.1016/j.jde.2019.01.031.

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Zhunussova, Zh Kh. "The surface to singular solitonic solution of the nonlinear Schrodinger equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 88, no. 4 (December 30, 2017): 26–33. http://dx.doi.org/10.31489/2017m4/26-33.

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Tekercioglu, Ramazan. "On the traveling wave solutions of pulse propagation in monomode fiber via the extended Kudryashov’s approach." Thermal Science 26, Spec. issue 1 (2022): 49–59. http://dx.doi.org/10.2298/tsci22s1049t.

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In this research paper, we tackle with the solitary wave solutions to the pulse prop?agation in monomode optic fiber by defining non-linear Schrodinger equation with higher order. We applied the extended Kudryashov?s method with Bernoulli-Riccati equation and successfully gained soliton solutions and their contour, 2-D and 3-D graphical representations, such as dark, singular, periodic and kink type solutions. We also discussed the obtained results in the related section.
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Lin, Yuanhua, and Liping He. "Existence of Traveling Wave Fronts for a Generalized Nonlinear Schrodinger Equation." Advances in Mathematical Physics 2022 (August 16, 2022): 1–6. http://dx.doi.org/10.1155/2022/9638150.

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In the presented paper, a generalized nonlinear Schr o dinger equation without delay convolution kernel and with special delay convolution kernel is investigated. By using the geometric singular perturbation theory, the existence of traveling wave fronts is proved. Firstly, we show that such traveling wave fronts exist without delay by non-Hamiltonian qualitative analysis. Then, for the generalized nonlinear Schr o dinger equation with a special local strong delay convolution kernel, the desired heteroclinic orbit is obtained by using the Fredholm theory.
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Vshivteev, A. S., N. V. Norin, and V. N. Sorokin. "Spectral problem for the Schrodinger equation with singular potential polynomial of even degree." Russian Physics Journal 39, no. 5 (May 1996): 442–56. http://dx.doi.org/10.1007/bf02436783.

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6

ESTEVEZ, P. G., and G. A. HERNAEZ. "Painleve Analysis and Singular Manifold Method for a (2 + 1) Dimensional Non-Linear Schrodinger Equation." Journal of Non-linear Mathematical Physics 8, Supplement (2001): 106. http://dx.doi.org/10.2991/jnmp.2001.8.supplement.19.

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7

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.
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Raza, Nauman, Riaz ur Rahman, Aly Seadawy, and Adil Jhangeer. "Computational and bright soliton solutions and sensitivity behavior of Camassa–Holm and nonlinear Schrödinger dynamical equation." International Journal of Modern Physics B 35, no. 11 (April 30, 2021): 2150157. http://dx.doi.org/10.1142/s0217979221501575.

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In this paper, we sketch and scrutinize the solitonic wave solution of Camassa–Holm equation by applying Kudryashov’s new method. We promote the algorithm of our new method to find the new solutions of this essential model. Camassa–Holm equation is a recent model in the point of distortion of hierarchies composition of integrability systems. It has been displayed that these solutions have the shape of dark, bright and singular solitons solutions of Camassa–Holm nonlinear Schrodinger equation. Graphically changing of extracted results of this model (CH) has been separated to grasp the substantial evolution. We analyze the sensitivity of the obtained solutions on behalf of different boundary conditions. It is fair that our model furnishes an impressive mathematical mechanism for manufacturing the solutions of the traveling wave for many models in physics and mathematics. The strategy utilized here is straightforward and succinct.
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Shalaby, A. M. "Dimensional Regularization of the Spatial wave function for a singular contact interaction in the Relativistic Schrodinger Equation." Journal of Physics: Conference Series 670 (January 25, 2016): 012045. http://dx.doi.org/10.1088/1742-6596/670/1/012045.

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CASAHORRÁN, J. "A NEW SUPERSYMMETRIC VERSION OF THE ABRAHAM-MOSES METHOD FOR SYMMETRIC POTENTIALS." Reviews in Mathematical Physics 08, no. 05 (July 1996): 655–68. http://dx.doi.org/10.1142/s0129055x96000226.

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Starting from the one-dimensional Schrodinger equation with symmetric potential Vs(x), a general method is presented in order to obtain a family of partially isospectral hamiltonians. Arguments concerning supersymmetric transformations, factorization procedures and Riccati equations are invoked along the article. As a result of the appearance of singular superpotentials, the physical meaning of our method can be summarized as follows: only the odd wave-functions of the original potential Vs(x) are transported via supersymmetry into the Hilbert space associated with the partner Vp(x). In such a case the degeneracy of energy levels is partially broken. Supersymmetry is neither exact nor spontaneously broken but realizes itself acting on wave functions vanishing at x=0. While the domain of the original hamiltonian H extends along the whole real axis, the susy partner Hp reduces to the half-line (x≤0 or x≥0). To illustrate how the procedure works in practice we resort to a symmetric potential in the Posch-Teller class containing both discrete and continuous spectra.
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Dissertations / Theses on the topic "Singular Schrodinger equation"

1

LIN, JIAN-HUNG, and 林建宏. "Singular Limit of the Nonlinear Schrodinger Equation." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/07313256463289097112.

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碩士
國立成功大學
數學系應用數學碩博士班
93
The purpose of this paper is to the study of singular limit for the convective NLS equation. 　First, we use two different methods to get conservation laws of the convective NLS equation. 　And then the local existence in time of the classical solutions can be established via an iteration method and the uniqueness of the solution is also proved. 　At last we prove the semiclassical limit of the solution.
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Baldelli, Laura. "Existence and multiplicity results for nonlinear elliptic problems." Doctoral thesis, 2022. http://hdl.handle.net/2158/1261959.

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In this work of thesis, we investigate existence and multiplicity results for a class of nonlinear elliptic problems. First, we deal with problems involving the p-Laplacian operator on bounded smooth domains, where a diffusion term appears into the nonlinearity. For this reason, variational methods cannot be used. Secondly, we treat existence and multiplicity of weak solutions for (p; q)- Laplacian equations, as well as for singular p-Laplacian Schrodinger equations, in the entire R^N whose nonlinearity combines a power-type term at critical level with a subcritical term, involving also nontrivial weights and a positive parameter. This latter case, considered also in a symmetric setting, allows us to use variational methods, but in the delicate situation of lack of compactness, so that classical results cannot be directly used, they need to be adapted.
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Books on the topic "Singular Schrodinger equation"

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Fibich, Gadi. Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse. Springer London, Limited, 2015.

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Fibich, Gadi. The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse. Springer, 2015.

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3

Fibich, Gadi. The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse. Springer, 2016.

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Book chapters on the topic "Singular Schrodinger equation"

1

Wang, Xiao-Ping. "Numerical Simulations of Singular Solutions of the Nonlinear Schrodinger Equations." In Effective Computational Methods for Wave Propagation, 7–32. Chapman and Hall/CRC, 2008. http://dx.doi.org/10.1201/9781420010879.ch1.

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Conference papers on the topic "Singular Schrodinger equation"

1

Deriglazov, Alexei. "On singular lagrangian underlying the Schrodinger equation." In 5th International School on Field Theory and Gravitation. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.081.0067.

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Radisavljevic-Gajic, Verica, Dimitrios A. Karagiannis, Meng-Bi Cheng, and Wu-Chung Su. "Recent Trends in Stabilization and Control of Distributed Parameter Dynamic Systems." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37151.

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The field of control and stabilization of distributed parameter systems described by partial differential equations has recently seen an increasing number of results published by very respected researchers in excellent control engineering and applied mathematics journals. This paper presents a survey of control and stabilization results with emphasis on controls. Various distributed parameter dynamic control and stabilization problems have been studied corresponding to heat conduction, wave propagation, Schrodinger equation, crowd (swarm) dynamics, magneto-hydro-dynamic channel flow, string and beam equations, viscous Burger equation, and general diffusion equations. Various techniques have been used for control and stabilization of such systems: Lyapunov stabilization, backstepping, gain scheduling, singular perturbations, sliding mode control, observer driven controller, tracking control, sampled-data control, neural networks. The field still remains widely open for future research. Applications of surveyed results to various areas including robots, aircraft, networks, transmission lines, electrochemical processes in energy systems are indicated.
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Journal articles
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