Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations

DOI10.1002/sapm1988783227zbMath0681.35087OpenAlexW2508061588MaRDI QIDQ4730199

Keti Tenenblat, Richard W. Beals

Publication date: 1988

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1988783227

zbMATH Keywords

Bäcklund transformationinverse scatteringgeneralized sine-Gordon equations

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05) Partial differential equations of mathematical physics and other areas of application (35Q99) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (10)

Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations ⋮ Fifth-order evolution equations describing pseudospherical surfaces ⋮ Submanifolds of constant sectional curvature in pseudo-Riemannian manifolds ⋮ On equations of type u x t=F(u,u x) which describe pseudospherical surfaces ⋮ Induced Surfaces and Their Integrable Dynamics ⋮ A note on solutions for the intrinsic generalized wave and sine-Gordon equations ⋮ INTRINSIC FORMULATION OF GEOMETRIC INTEGRABILITY AND ASSOCIATED RICCATI SYSTEM GENERATING CONSERVATION LAWS ⋮ Twisted hierarchies associated with the generalized sine-Gordon equation ⋮ On the symmetry groups of the intrinsic generalized wave and sine–Gordon equations ⋮ A twisted integrable hierarchy with $\mathbb D_2$D2 symmetry

Cites Work

• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• On the Solution of the Generalized Wave and Generalized Sine-Gordon Equations
• Scattering and inverse scattering for first order systems
• Inverse scattering and evolution equations
• Scattering and inverse scattering for first-order systems: II
• Inverse scattering and the boussinesq equation
• Inverse scattering on the line
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation

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