Method of Solution for a Class of Multidimensional Nonlinear Evolution Equations
- 4 July 1983
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 51 (1), 7-10
- https://doi.org/10.1103/physrevlett.51.7
Abstract
A general method is given for solving certain inverse problems in the plane. The results can be used to construct the solution to the initial-value problems of related nonlinear evolution equations in two spatial and one temporal dimension. The method also allows one to compute lumps, i.e., multidimensional solitons tending to zero in all spatial directions.Keywords
This publication has 17 references indexed in Scilit:
- Scattering and inverse scatering for first-order systemsSurveys in Differential Geometry, 1998
- Solitons and the Inverse Scattering TransformPublished by Society for Industrial & Applied Mathematics (SIAM) ,1981
- The resolvent and Hamiltonian systemsFunctional Analysis and Its Applications, 1977
- Nonlinear Evolution Equations—Two and Three DimensionsPhysical Review Letters, 1975
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974
- Korteweg‐devries equation and generalizations. VI. methods for exact solutionCommunications on Pure and Applied Mathematics, 1974
- Nonlinear-Evolution Equations of Physical SignificancePhysical Review Letters, 1973
- Method for Solving the Sine-Gordon EquationPhysical Review Letters, 1973
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967