Periodic and hyperbolic soliton solutions of a number of nonlocal nonlinear equations
From MaRDI portal
Publication:5245226
DOI10.1063/1.4914335zbMath1320.35146arXiv1405.5267OpenAlexW177104481MaRDI QIDQ5245226
Publication date: 7 April 2015
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.5267
Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear higher-order PDEs (35G20) Elliptic functions and integrals (33E05) Soliton solutions (35C08)
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Cites Work
- The reduction problem and the inverse scattering method
- To the integrability of the system of two coupled nonlinear Schrödinger equations
- Nonlinear differential–difference equations and Fourier analysis
- Exact solutions of the saturable discrete nonlinear Schrödinger equation
- Physical realization of -symmetric potential scattering in a planar slab waveguide
- Superposition of elliptic functions as solutions for a large number of nonlinear equations