Integration of a loaded Korteweg-de Vries equation in a class of periodic functions

DOI10.3103/S1066369X16020110zbMath1342.35315MaRDI QIDQ283090

M. M. Matyokubov, Alisher B. Yakhshimuratov

Publication date: 13 May 2016

Published in: Russian Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sturm-Liouville operatorinverse spectral problemKorteweg-de Vries equationtrace formulassystem of equations of Dubrovin

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Sturm-Liouville theory (34B24) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (7)

Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions ⋮ On complex-valued solutions of the general loaded Korteweg-de Vries equation with a source ⋮ Integration of the general loaded Korteweg-de Vries equation with an integral type source in the class of rapidly decreasing complex-valued functions ⋮ Unnamed Item ⋮ Integration of the nonlinear Schrödinger equation with an additional term in the class of periodic functions ⋮ 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

Cites Work

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• The Korteweg-de Vries equation with a self-consistent source in the class of periodic functions
• A generalization of Borg's inverse theorem for Hill's equations
• The periodic problem for the Korteweg-de Vries equation
• Integrating the Korteweg-de Vries equation with a self-consistent source and ``steplike initial data
• Additional symmetries for integrable equations and conformal algebra representation
• Solution of an initial-boundary value problem for coupled nonlinear waves
• Spectral conservation laws for periodic nonlinear equations of the Melnikov type
• Integration of the nonlinear Schrodinger equation with a source
• Periodic solutions of the KdV equation
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
• The inverse problem for periodic potentials

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