Solutions with functional parameters of \(2+1\)-dimensional integrable nonlinear equations. Two dimensional integrable generalization of the Kaup-Kupershmidt equation

DOI10.1007/s11182-015-0592-8zbMath1384.37096OpenAlexW2318698339MaRDI QIDQ1742302

M. Yu. Basalaev, A. V. Topovsky, V. G. Dubrovskij

Publication date: 11 April 2018

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

Full work available at URL: https://doi.org/10.1007/s11182-015-0592-8

zbMATH Keywords

periodic solutionsintegrable nonlinear equationssolutions with functional parametersthe \( \overline{\partial} \)-dressing methodtwo-dimensional integrable generalization of the Kaup-Kupershmidt equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08)

Cites Work

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• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• The D-bar approach to inverse scattering and nonlinear evolutions
• Soliton solutions and symmetries of the \(2+1\) dimensional Kaup-Kupershmidt equation
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• Linear spectral problems, non-linear equations and the δ-method
• The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via \(\overline \partial\)-dressing method

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