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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Athorne, C. "A Toda system." Physics Letters A 206, no. 3-4 (October 1995): 162–66. http://dx.doi.org/10.1016/0375-9601(95)00643-h.

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2

Talalaev, D. V. "Quantum generalized Toda system." Theoretical and Mathematical Physics 171, no. 2 (May 2012): 691–99. http://dx.doi.org/10.1007/s11232-012-0066-x.

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3

Doliwa, Adam. "Geometric discretisation of the Toda system." Physics Letters A 234, no. 3 (September 1997): 187–92. http://dx.doi.org/10.1016/s0375-9601(97)00477-5.

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4

Konno, Kimiaki. "Complex Dynamical System for Toda Lattice." Journal of the Physical Society of Japan 57, no. 11 (November 15, 1988): 3707–13. http://dx.doi.org/10.1143/jpsj.57.3707.

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5

Itoyama, H. "Symmetries of the generalized Toda system." Physics Letters A 140, no. 7-8 (October 1989): 391–94. http://dx.doi.org/10.1016/0375-9601(89)90073-x.

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6

del Pino, Manuel, Michal Kowalczyk, and Juncheng Wei. "The Jacobi-Toda system and foliated interfaces." Discrete & Continuous Dynamical Systems - A 28, no. 3 (2010): 975–1006. http://dx.doi.org/10.3934/dcds.2010.28.975.

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7

Sciacca, Vincenzo. "DiscreteKPEquation and Momentum Mapping of Toda System." Journal of Nonlinear Mathematical Physics 10, sup2 (January 2003): 209–22. http://dx.doi.org/10.2991/jnmp.2003.10.s2.17.

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8

Doyon, Benjamin. "Generalized hydrodynamics of the classical Toda system." Journal of Mathematical Physics 60, no. 7 (July 2019): 073302. http://dx.doi.org/10.1063/1.5096892.

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9

Ao, Weiwei, and Liping Wang. "New concentration phenomena forSU(3)Toda system." Journal of Differential Equations 256, no. 4 (February 2014): 1548–80. http://dx.doi.org/10.1016/j.jde.2013.11.006.

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10

Chernyakov, Yu B., G. I. Sharygin, and A. S. Sorin. "Bruhat Order in Full Symmetric Toda System." Communications in Mathematical Physics 330, no. 1 (April 20, 2014): 367–99. http://dx.doi.org/10.1007/s00220-014-2035-8.

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11

Gladiali, Francesca, Massimo Grossi, and Juncheng Wei. "On a general SU(3) Toda system." Calculus of Variations and Partial Differential Equations 54, no. 4 (August 15, 2015): 3353–72. http://dx.doi.org/10.1007/s00526-015-0906-2.

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12

Ao, Weiwei, Chang-Shou Lin, and Juncheng Wei. "On Toda system with Cartan matrix $G_2$." Proceedings of the American Mathematical Society 143, no. 8 (April 9, 2015): 3525–36. http://dx.doi.org/10.1090/proc/12558.

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13

Wei, Juncheng, Chunyi Zhao, and Feng Zhou. "On nondegeneracy of solutions to Toda system." Comptes Rendus Mathematique 349, no. 3-4 (February 2011): 185–90. http://dx.doi.org/10.1016/j.crma.2010.11.025.

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14

Saveliev, Mikhail V., and Svetlana A. Savelieva. "W∞-geometry and associated continuous Toda system." Physics Letters B 313, no. 1-2 (August 1993): 55–58. http://dx.doi.org/10.1016/0370-2693(93)91190-x.

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15

Jimbo, Michio. "QuantumR matrix for the generalized Toda system." Communications in Mathematical Physics 102, no. 4 (December 1986): 537–47. http://dx.doi.org/10.1007/bf01221646.

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16

Nimmo, J. J. C., and R. Willox. "Darboux transformations for the two-dimensional Toda system." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 453, no. 1967 (December 8, 1997): 2497–525. http://dx.doi.org/10.1098/rspa.1997.0133.

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17

Jost, Jürgen, Chunqin Zhou, and Miaomiao Zhu. "The super-Toda system and bubbling of spinors." Journal of Functional Analysis 276, no. 2 (January 2019): 410–46. http://dx.doi.org/10.1016/j.jfa.2018.07.002.

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18

Satija, I. I., A. R. Bishop, and K. Fesser. "Chaos in a damped and driven toda system." Physics Letters A 112, no. 5 (October 1985): 183–87. http://dx.doi.org/10.1016/0375-9601(85)90498-0.

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19

Rañada, Manuel F. "A new integrable Toda‐related three‐particle system." Journal of Mathematical Physics 35, no. 12 (December 1994): 6577–83. http://dx.doi.org/10.1063/1.530692.

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20

Ohtsuka, Hiroshi, and Takashi Suzuki. "Blow-up analysis for SU(3) Toda system." Journal of Differential Equations 232, no. 2 (January 2007): 419–40. http://dx.doi.org/10.1016/j.jde.2006.09.003.

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21

Yamazaki, Masahito. "Quantum trilogy: discrete Toda, Y-system and chaos." Journal of Physics A: Mathematical and Theoretical 51, no. 5 (January 4, 2018): 053002. http://dx.doi.org/10.1088/1751-8121/aaa08e.

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22

J. Hansen, P., and D. J. Kaup. "The Toda Lattice as a Forced Integrable System." Journal of the Physical Society of Japan 54, no. 11 (November 15, 1985): 4126–32. http://dx.doi.org/10.1143/jpsj.54.4126.

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23

J. Hansen, P., and D. J. Kaup. "The Toda Lattice as a Forced Integrable System." Journal of the Physical Society of Japan 55, no. 1 (January 15, 1986): 433. http://dx.doi.org/10.1143/jpsj.55.433.

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24

Zhang, Yufeng, Xiangzhi Zhang, Yan Wang, and Jiangen Liu. "Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws." Zeitschrift für Naturforschung A 72, no. 1 (January 1, 2017): 77–86. http://dx.doi.org/10.1515/zna-2016-0347.

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Анотація:

AbstractWith the help ofR-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula byR-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

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25

Li, Chuanzhong. "Constrained lattice-field hierarchies and Toda system with Block symmetry." International Journal of Geometric Methods in Modern Physics 13, no. 05 (April 21, 2016): 1650061. http://dx.doi.org/10.1142/s0219887816500614.

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Анотація:

In this paper, we construct the additional [Formula: see text]-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new integrable difference equations. Under a further reduction, the constrained two-lattice integrable systems can be combined into one single integrable system, namely the well-known one-dimensional original Toda hierarchy. We prove that the one-dimensional original Toda hierarchy has a nice Block Lie symmetry.

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26

MAKAROV, V. A., W. EBELING, and M. G. VELARDE. "SOLITON-LIKE WAVES ON DISSIPATIVE TODA LATTICES." International Journal of Bifurcation and Chaos 10, no. 05 (May 2000): 1075–89. http://dx.doi.org/10.1142/s0218127400000761.

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Анотація:

Dissipative soliton-like waves in 1D Toda lattices generated by suitable energy supply from external sources have been studied. Using the general theory of canonical-dissipative systems we have constructed a special canonical-dissipative system whose solution starting from an arbitrarily initial condition decays to a solution of the standard, conservative Toda system. The energy of the final state may be prescribed beforehand. We have also studied the influence of noise and have calculated the distribution of probability density in phase space and the energy distribution. Other noncanonical models of energy input, including nonlinear nearest neighbor coupling and "Rayleigh" friction, have been analyzed. We have shown under what conditions the lattices can sustain the propagation of stable solitary waves and wave trains.

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27

Li, Chuanzhong, and Anni Meng. "On the Full-Discrete Extended Generalised q-Difference Toda System." Zeitschrift für Naturforschung A 72, no. 8 (August 28, 2017): 703–9. http://dx.doi.org/10.1515/zna-2017-0113.

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AbstractIn this paper, we construct a full-discrete integrable difference equation which is a full-discretisation of the generalised q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of an extended generalised full-discrete q-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the extended full-discrete generalised q-Toda hierarchy are given.

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28

Hamedi-Nezhad, S., M. Zalani Sofla, L. Kavitha, and V. Senthil Kumar. "New Rational Solutions for Relativistic Discrete Toda Lattice System." Communications in Theoretical Physics 62, no. 3 (September 2014): 363–72. http://dx.doi.org/10.1088/0253-6102/62/3/13.

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29

Saveliev, M. V. "On the integrability problem of a continuous Toda system." Theoretical and Mathematical Physics 92, no. 3 (September 1992): 1024–31. http://dx.doi.org/10.1007/bf01017079.

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30

D'Aprile, Teresa, Angela Pistoia, and David Ruiz. "Asymmetric blow-up for the SU(3) Toda system." Journal of Functional Analysis 271, no. 3 (August 2016): 495–531. http://dx.doi.org/10.1016/j.jfa.2016.04.007.

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31

Saveliev, M. V. "On some integrable generalizations of the continuous Toda system." Theoretical and Mathematical Physics 108, no. 2 (August 1996): 1003–12. http://dx.doi.org/10.1007/bf02070671.

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32

Battaglia, Luca. "Existence and multiplicity result for the singular Toda system." Journal of Mathematical Analysis and Applications 424, no. 1 (April 2015): 49–85. http://dx.doi.org/10.1016/j.jmaa.2014.10.081.

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33

Hyder, Ali, Changshou Lin, and Juncheng Wei. "The SU(3) Toda system with multiple singular sources." Pacific Journal of Mathematics 305, no. 2 (April 29, 2020): 645–66. http://dx.doi.org/10.2140/pjm.2020.305.645.

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34

Darvishi, M. T., and F. Khani. "New Exact Solutions of a Relativistic Toda Lattice System." Chinese Physics Letters 29, no. 9 (September 2012): 094101. http://dx.doi.org/10.1088/0256-307x/29/9/094101.

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35

Zhu, Xiao Bao. "Solutions for Toda system on Riemann surface with boundary." Acta Mathematica Sinica, English Series 27, no. 8 (July 15, 2011): 1501–20. http://dx.doi.org/10.1007/s10114-011-9532-x.

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36

Pei, Rui Chang. "A remark on the generalized second order Toda system." Acta Mathematica Sinica, English Series 29, no. 9 (August 15, 2013): 1691–702. http://dx.doi.org/10.1007/s10114-013-2080-9.

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37

Wang, Kelei. "Stable and finite Morse index solutions of Toda system." Journal of Differential Equations 268, no. 1 (December 2019): 60–79. http://dx.doi.org/10.1016/j.jde.2019.08.006.

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38

Vinogradov, G. A., M. M. El'yashevich, and V. N. Likhachev. "On ergodicity of an integrable system (the Toda chain)." Physics Letters A 151, no. 9 (December 1990): 515–18. http://dx.doi.org/10.1016/0375-9601(90)90471-y.

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39

Ge, Mo-Lin, and Kang Xue. "Braid group representations related to the generalized toda system." Physics Letters A 146, no. 5 (May 1990): 245–51. http://dx.doi.org/10.1016/0375-9601(90)90973-r.

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40

Legaré, M. "On Lax pairs and matrix extended simple Toda systems." International Journal of Mathematics and Mathematical Sciences 2005, no. 17 (2005): 2735–47. http://dx.doi.org/10.1155/ijmms.2005.2735.

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41

Henrici, Andreas. "Nekhoroshev Stability for the Dirichlet Toda Lattice." Symmetry 10, no. 10 (October 16, 2018): 506. http://dx.doi.org/10.3390/sym10100506.

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Анотація:

In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one.

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42

Lee, Youngae, Chang-Shou Lin, Juncheng Wei, and Wen Yang. "Degree counting and Shadow system for Toda system of rank two: One bubbling." Journal of Differential Equations 264, no. 7 (April 2018): 4343–401. http://dx.doi.org/10.1016/j.jde.2017.12.018.

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43

AVAN, J. "GENERALIZED TODA AND VOLTERRA MODELS." International Journal of Modern Physics A 07, no. 20 (August 10, 1992): 4855–69. http://dx.doi.org/10.1142/s0217751x92002192.

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Анотація:

The mean procedure of Faddeev-Reshetikhin with non-Abelian automorphism groups is applied to construct generalizations of the open Toda sl(n, C) chain. These models admit a consistent reduction to integrable generalized Volterra models. An example of such models is analyzed: it leads in the continuum limit to the [Formula: see text] Hirota differential system, associated with two-matrix models of discrete gravity. The continuum limit of the general Volterra models and their relation with discretized versions of Wn-algebra are analyzed.

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44

CUCCOLI, ALESSANDRO, ROBERTO LIVI, MAURO SPICCI, VALERIO TOGNETTI, and RUGGERO VAIA. "THERMODYNAMICS OF THE TODA CHAIN." International Journal of Modern Physics B 08, no. 18 (August 15, 1994): 2391–446. http://dx.doi.org/10.1142/s021797929400097x.

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Анотація:

A review of the classical and quantum thermodynamic properties of the Toda chain is provided, together with a survey of the techniques that have been used to work them out, i.e., the bilateral Laplace transform method for the classical system, the Bethe–Ansatz and the variational path-integral approach for the quantum one. For the classical Toda chain we also recall some of the main dynamical features, i.e. the integrability of the model and the soliton-like solutions of the equations of motion. In the quantum case a comparison between the Bethe–Ansatz and the variational method is made. In particular it is shown as the latter offers the possibility of also evaluating static correlation functions.

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45

Liu, Yong. "Even solutions of the Toda system with prescribed asymptotic behavior." Communications on Pure and Applied Analysis 10, no. 6 (May 2011): 1779–90. http://dx.doi.org/10.3934/cpaa.2011.10.1779.

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46

Ao, Weiwei. "Sharp estimates for fully bubbling solutions of $B_2$ Toda system." Discrete and Continuous Dynamical Systems 36, no. 4 (September 2015): 1759–88. http://dx.doi.org/10.3934/dcds.2016.36.1759.

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47

Kashaev, R. M., and N. Reshetikhin. "Affine Toda Field Theory as a 3-Dimensional Integrable System." Communications in Mathematical Physics 188, no. 2 (September 1, 1997): 251–66. http://dx.doi.org/10.1007/s002200050164.

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48

Chae, Dongho, Hiroshi Ohtsuka, and Takashi Suzuki. "Some existence results for solutions to SU(3) Toda system." Calculus of Variations and Partial Differential Equations 24, no. 4 (October 18, 2005): 403–29. http://dx.doi.org/10.1007/s00526-005-0326-9.

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49

Battaglia, Luca, and Gabriele Mancini. "A note on compactness properties of the singular Toda system." Rendiconti Lincei - Matematica e Applicazioni 26, no. 3 (2015): 299–307. http://dx.doi.org/10.4171/rlm/708.

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50

Tsuda, Teruhisa. "Toda equation and special polynomials associated with the Garnier system." Advances in Mathematics 206, no. 2 (November 2006): 657–83. http://dx.doi.org/10.1016/j.aim.2005.10.006.

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