An inverse scattering scheme for the regularized long-wave equation

DOI10.1063/1.533278zbMath0973.35165OpenAlexW2028616158MaRDI QIDQ2737976

John M. Dye, Allen Parker

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533278

zbMATH Keywords

explicit solutionsdressing methodregularized long-wave equationshallow water wave equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

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Cites Work

• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
• Solitary-wave interaction
• Inverse scattering and the boussinesq equation
• Painlevé analysis and Lie group symmetries of the regularized long-wave equation
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• Euler operators and conservation laws of the BBM equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Regularized long wave equation and inverse scattering transform
• On the Nonexistence of Soliton Solutions of the Regularized Long-Wave Equation
• Hydrodynamic Foundation and Painlevé Analysis of Hirota-Satsuma-Type Equations
• On exact solutions of the regularized long-wave equation: A direct approach to partially integrable equations. I. Solitary wave and solitons
• Integrals of nonlinear equations of evolution and solitary waves
• Model equations for long waves in nonlinear dispersive systems