Generalization of the inverse scattering problem method

DOI10.1007/BF01028614zbMath0413.47006MaRDI QIDQ1260574

S. V. Manakov, Vladimir E. Zakharov

Publication date: 1977

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse scattering problem

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Scattering theory of linear operators (47A40) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Related Items (7)

Geometry and analysis on isospectral sets. I: Riemannian geometry, asymptotic case ⋮ Asymptotic \(m\)-phase soliton-type solutions of a singularly perturbed Korteweg-de Vries equation with variable coefficients ⋮ Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II ⋮ Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric ∂̄-dressing ⋮ Families of particular solutions to multidimensional partial differential equations ⋮ General structure of nonlinear evolution equations in 1+2 dimensions integrable by the two-dimensional Gelfand-Dickey-Zakharov-Shabat spectral problem and their transformation properties ⋮ On the stability of nonlinear waves in integrable models

Cites Work

• Method for Solving the Korteweg-deVries Equation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
• Integrals of nonlinear equations of evolution and solitary waves

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