Inverse problem forN ×N hyperbolic systems on the plane and the N-wave interactions

DOI10.1002/cpa.3160440503zbMath0737.35118OpenAlexW1968882114MaRDI QIDQ3974411

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Publication date: 25 June 1992

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160440503

zbMATH Keywords

inverse scattering transformCauchy problemsnonlinear evolution equationssolution conditions\(N\)-wave interactions equation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Riemann-Hilbert problems in context of PDEs (35Q15) First-order hyperbolic systems (35L40)

Related Items (10)

Inverse scattering problem for nonstationary Dirac-type systems on the half-plane ⋮ The dressing method and nonlocal Riemann-Hilbert problems ⋮ Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition ⋮ Inverse nonstationary scattering for the linear system of the 3-wave interaction problem in the case of two incident waves with the same velocity ⋮ Inverse scattering transform in two spatial dimensions for the \(N\)-wave interaction problem with a dispersive term ⋮ On the integrability of linear and nonlinear partial differential equations ⋮ Inverse scattering problem for nonstationary Dirac-type systems on the plane ⋮ Inverse scattering problem for linear system of four-wave interaction problem with equal number of incident and scattered waves ⋮ Forced (2 + 1)-dimensional discrete three-wave equation ⋮ Nonlinear constraints and soliton solutions of 1+2-dimensional three-wave equation

Cites Work

• The inverse scattering solution for the full three dimensional three-wave resonant interaction

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