Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions

DOI10.35634/vm230111zbMath1527.35355OpenAlexW4362637669MaRDI QIDQ6175506

Unnamed Author, Unnamed Author

Publication date: 18 August 2023

Published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vuu842

zbMATH Keywords

Jost solutionsinverse scattering problemevolution of scattering dataGelfand-Levitan-Marchenko integral equationloaded Korteweg-de Vries equation

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Sturm-Liouville theory (34B24) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Cites Work

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• Propagation of nonlinear waves in a gas-liquid medium. Exact and approximate analytical solutions of wave equations
• Periodic Toda chain with an integral source
• New exact solutions for a generalized KdV equation
• Integration of a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions
• Integration of the nonlinear Korteweg-de Vries equation with an additional term
• Initial-boundary problem for parabolic-hyperbolic equation with loaded summands
• Integration of the Korteweg-de Vries equation with a source
• Solution of an initial-boundary value problem for coupled nonlinear waves
• Method for Solving the Korteweg-deVries Equation
• Nonlinear resonant scattering and plasma instability: an integrable model
• Numerical solution of a boundary value problem for a loaded parabolic equation with nonlocal boundary conditions
• Nonlocal problem with the integral condition for a loaded heate equation
• Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions
• Integration of higher Korteweg-de Vries equation with a self-consistent source in class of periodic functions
• Integrals of nonlinear equations of evolution and solitary waves
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
• ON INTEGRATION OF THE LOADED KORTEWEG-DE VRIES EQUATION IN THE CLASS OF RAPIDLY DECREASING FUNCTIONS
• Integrating the loaded KdV equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions
• Negative-order KdV equations in (3+1) dimensions by using the KdV recursion operator