Decay mode solution of the two-dimensional KdV equation and the generalized Bäcklund transformation

DOI10.1063/1.524804zbMath0491.35072OpenAlexW2001692396MaRDI QIDQ3952523

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Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.524804

zbMATH Keywords

Bäcklund transformationsoliton solutioncompletely integrable systemnonlinear superpositionexplode-decay modeinfinite life timenon- soliton part

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (12)

Nonlinear superposition formula of the Boussinesq hierachy ⋮ Rare decaying ripple solutions within the KP equation ⋮ The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation ⋮ A Bäcklund transformation and nonlinear superposition formula of a modified Korteweg–de Vries-type bilinear equation ⋮ The decay mode solutions for the cylindrical KP equation ⋮ Soliton-like structures and the connection between the Bq and KP equations ⋮ Integrable discretization of soliton equations via bilinear method and Bäcklund transformation ⋮ Evolution of lump solutions for the KP equation ⋮ Nondegeneracy, Morse index and orbital stability of the KP-I lump solution ⋮ Similarity, Bäcklund transformations and rational solutions ⋮ Simple multiple explode–decay mode solutions of a two-dimensional nonlinear Schrödinger equation ⋮ The higher-order KdV equation with a source and nonlinear superposition formula.

Cites Work

• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Shallow Water Waves Propagating along Undulation of Bottom Surface
• N-Soliton Solution of the Two-Dimensional Korteweg-deVries Equation
• Bäcklund Transformation of the Cylindrical KdV Equation
• A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
• Similarity Solutions of Some Two-Space-Dimensional Nonlinear Wave Evolution Equations
• Soliton Interactions in Two Dimensions
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• Asymptotic Solutions of the Korteweg-deVries Equation
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• The decay of the continuous spectrum for solutions of the Korteweg-deVries equation

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