Boundary value problems for the \(N\)-wave interaction equations

DOI10.1016/j.physleta.2009.03.064zbMath1229.35142OpenAlexW2049655405MaRDI QIDQ653135

Beatrice Pelloni, Dimitrios A. Pinotsis

Publication date: 6 January 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2009.03.064

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) General spectral theory of ordinary differential operators (34L05) Initial value problems for second-order hyperbolic equations (35L15) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

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The three-wave equation on the half-line ⋮ Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane

Cites Work

• The inverse scattering solution for the full three dimensional three-wave resonant interaction
• Exact solutions of the 3-wave resonant interaction equation
• Universality and integrability of the nonlinear evolution PDE’s describing N-wave interactions
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• Scattering and inverse scattering for first order systems
• Scattering and inverse scattering for first-order systems: II
• Linear spectral problems, non-linear equations and the δ-method