Integration of the nonlinear Schrödinger equation with an additional term in the class of periodic functions

DOI10.1134/S0040577919040044zbMath1428.35513OpenAlexW2945844750MaRDI QIDQ2286721

Yanyan Li

Publication date: 22 January 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577919040044

zbMATH Keywords

Dirac operatornonlinear Schrödinger equationinverse spectral problemtrace formulaDubrovin equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Sturm-Liouville theory (34B24) NLS equations (nonlinear Schrödinger equations) (35Q55)

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Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions ⋮ On the modified Korteweg-de-Vries equation with loaded term ⋮ Cauchy problem for the nonlinear Hirota equation in the class of periodic infinite-zone functions ⋮ Integration of the Kaup-Boussinesq system with time-dependent coefficients ⋮ Cauchy problem for the nonlinear Liouville equation in the class of periodic infinite-gap functions ⋮ Integration of the modified Korteweg-de Vries-Liouville equation in the class of periodic infinite-gap functions

Cites Work

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• Integration of a loaded Korteweg-de Vries equation in a class of periodic functions
• The nonlinear Schrödinger equation with a self-consistent source in the class of periodic functions
• The Korteweg-de Vries equation with a self-consistent source in the class of periodic functions
• Integration of the sine-Gordon equation with a self-consistent source of the integral type in the case of multiple eigenvalues
• On integration of Korteweg-de Vries equation in a class of rapidly decreasing complex-valued functions
• On the sine-Gordon equation with a self-consistent source corresponding to multiple eigenvalues
• Method for Solving the Korteweg-deVries Equation
• Spectral conservation laws for periodic nonlinear equations of the Melnikov type
• ELLIPTIC SOLUTIONS OF THE NONLINEAR SCHRÖDINGER EQUATION AND THE MODIFIED KORTEWEG-DE VRIES EQUATION
• Instability zones of periodic 1-dimensional Schrödinger and Dirac operators
• Integrals of nonlinear equations of evolution and solitary waves
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation