Toward a General Solution of the Three-Wave Partial Differential Equations

DOI10.1111/SAPM.12133zbMath1346.35192OpenAlexW2473550892MaRDI QIDQ2816386

Harvey Segur, Ruth A. Martin

Publication date: 22 August 2016

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

Full work available at URL: https://doi.org/10.1111/sapm.12133

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) PDEs in connection with statistical mechanics (35Q82)

Related Items (3)

Novel soliton solutions for the fractional three-wave resonant interaction equations ⋮ Semiclassical soliton ensembles for the three-wave resonant interaction equations ⋮ Preface: Mark J. Ablowitz, nonlinear waves and integrable systems. Part I

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• The sine-Gordon equations: Complete and partial integrability
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• The Painlevé property for partial differential equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. II
• A Method for Solvithe Separable Initial-Value Problem of the Full Three-Dimensional Three-Wave Interaction
• The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability
• Blow-up Surfaces for Nonlinear Wave Equations, I
• Blow-up surfaces for nonlinear wave equations, II
• Bäcklund transformation and the Painlevé property
• The structure of WTC expansions and applications
• A method of proving the convergence of the Painleve expansions of partial differential equations

This page was built for publication: Toward a General Solution of the Three-Wave Partial Differential Equations