Symmetries, exact solutions, and nonlinear superposition formulas for two integrable partial differential equations

DOI10.1063/1.533373zbMath0999.37052OpenAlexW2025555085MaRDI QIDQ2738075

Pilar Ruiz Gordoa

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533373

zbMATH Keywords

nonlinear superposition principleDarboux transformationinvariant solutionsmultisoliton solutionsintegrable sixth-order 1+1-dimensional nonlinear equation

Mathematics Subject Classification ID

Related Items (5)

Analytical and numerical studying of the perturbed Korteweg-de Vries equation ⋮ Painlevé analysis, infinite dimensional symmetry group and symmetry reductions for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation ⋮ Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1 ⋮ Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation ⋮ A linear algebraic nonlinear superposition formula

Uses Software

• SYMMGRP.MAX

Cites Work

• Symbolic methods to construct exact solutions of nonlinear partial differential equations
• Inverse scattering method with variable spectral parameter
• The computer calculation of Lie point symmetries of large systems of differential equations
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• Some results on the Caudrey-Dodd-Gibbon-Kotera-Sawada equation
• Non-isospectral deformations and Darboux transformations for the third-order spectral problem
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Wave solutions of a (2+1)-dimensional generalization of the nonlinear Schr dinger equation
• A new hierarchy of Korteweg–de Vries equations
• On a shallow water wave equation
• On a new non-isospectral variant of the Boussinesq hierarchy
• Nonisospectral scattering problems: A key to integrable hierarchies
• Breaking solitons in 2+1-dimensional integrable equations
• Hyperelliptic asymptotics of Painlevé-type equations
• Symmetries of a (2+1)-dimensional breaking soliton equation
• The singular manifold method revisited

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