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Spectral analysis of generalized Volterra equation |
Junyi ZHU1, Xinxin MA1, Zhijun QIAO2( ) |
1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX 78539, USA |
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Abstract A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform. The two-sheeted Riemann surface associated with the boundary problem is transformed into the Riemann sphere by introducing a suitable variable transformation. The associated spectral properties of the lattice in single-valued variable was discussed. The constraint condition about the nonzero boundary condition and the scattering data is found.
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Volterra lattice
nonzero boundary condition
inverse scattering transform
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Corresponding Author(s):
Zhijun QIAO
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Issue Date: 22 November 2019
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| 1 |
M J Ablowitz, G Biondini, B Prinari. Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions. Inverse Problems, 2007, 23: 1711–1758
https://doi.org/10.1088/0266-5611/23/4/021
|
| 2 |
G Biondini, G Kovačić. Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions. J Math Phys, 2014, 55: 031506
https://doi.org/10.1063/1.4868483
|
| 3 |
H H Dai, X G Geng. Decomposition of a 2+ 1-dimensional Volterra type lattice and its quasi-periodic solutions. Chaos Solitons Fractals, 2003, 18: 1031–1044
https://doi.org/10.1016/S0960-0779(03)00061-4
|
| 4 |
X G Geng, H Liu. The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation. J Nonlinear Sci, 2018, 28: 739–763
https://doi.org/10.1007/s00332-017-9426-x
|
| 5 |
R Hirota, J Satsuma. N-soliton solution of non-linear network equations describing a Volterra system. J Phys Soc Japan, 1976, 40: 891–900
https://doi.org/10.1143/JPSJ.40.891
|
| 6 |
M Kac, P van Moerbeke. On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices. Adv Math, 1975, 16: 160–169
https://doi.org/10.1016/0001-8708(75)90148-6
|
| 7 |
S Manakov. Complete integrability and stochastization of discrete dynamical systems. Sov Phys JETP, 1974, 40: 269–274
|
| 8 |
Y B Suris. The Problem of Integrable Discretization: Hamiltonian Approach. Basel: Birkhäuser Verlag, 2003
https://doi.org/10.1007/978-3-0348-8016-9
|
| 9 |
V E Vekslerchik. Explicit solutions for a (2+ 1)-dimensional Toda-like chain. J Phys A: Math Gen, 2013, 46: 055202
https://doi.org/10.1088/1751-8113/46/5/055202
|
| 10 |
J Wei, X G Geng. A vector generalization of Volterra type differential-difference equations. Appl Math Lett, 2016, 55: 36–41
https://doi.org/10.1016/j.aml.2015.11.008
|
| 11 |
Y T Wu, D L Du. On the Lie-Poisson structure of the nonlinearized discrete eigenvalue problem. J Math Phys, 2000, 41: 5832–5848
https://doi.org/10.1063/1.533440
|
| 12 |
Y T Wu, X G Geng. A new hierarchy of integrable differential-difference equations and Darboux transformation. J Phys A: Math Gen, 1998, 31: L677–L684
https://doi.org/10.1088/0305-4470/31/38/004
|
| 13 |
Y Zeng, S Rauch-Wojciechowski. Continuous limits for the Kac-Van Moerbeke hierarchy and for their restricted flows. J Phys A: Math Gen, 1995, 28: 3825–3840
https://doi.org/10.1088/0305-4470/28/13/026
|
| 14 |
J Y Zhu, L L Wang, X G Geng. Riemann-Hilbert approach to the TD equation with nonzero boundary condition. Front Math China, 2018, 13: 1245–1265
https://doi.org/10.1007/s11464-018-0729-5
|
| 15 |
J Y Zhu, L L Wang, Z J Qiao. Inverse spectral transform for the Ragnisco-Tu equation with Heaviside initial condition. J Math Anal Appl, 2019, 474: 452–466
https://doi.org/10.1016/j.jmaa.2019.01.054
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