Painleve property and pseudopotentials for nonlinear evolution equations
- 7 August 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (15) , 2897-2913
- https://doi.org/10.1088/0305-4470/22/15/009
Abstract
The link between the singularity manifold equation and the pseudopotential equations is found for nonlinear evolution equations both in 1+1 and 2+1 dimensions. Many examples are given: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Harry Dym, a higher-order Korteweg-de Vries, Sawada-Kotera, Kaup-Kuperschmidt, Kadomtsev-Petviashvili, Boussinesq, modified Kadomtsev-Petviashvili, and (2+1)-dimensional Sawada-Kotera equations.Keywords
This publication has 16 references indexed in Scilit:
- Pseudopotentials for non-linear evolution equations in 2 + 1 dimensionsInternational Journal of Non-Linear Mechanics, 1988
- Pseudopotentials, Lax equations and Backlund transformations for nonlinear evolution equationsJournal of Physics A: General Physics, 1988
- On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchiesPhysica Scripta, 1987
- The Harry Dym equation in 2+1 dimensions: A reciprocal link with the Kadomtsev-Petviashvili equationPhysics Letters A, 1987
- On Reciprocal Bäcklund Transformations and the Korteweg-deVries HierarchyPhysica Scripta, 1986
- On Reciprocal Bäcklund Transformations of Inverse Scattering SchemesPhysica Scripta, 1984
- Soliton solutions and the higher order Korteweg–de Vries equationsJournal of Mathematical Physics, 1977
- Prolongation structures and nonlinear evolution equations in two spatial dimensionsJournal of Mathematical Physics, 1976
- Prolongation structures and a generalized inverse scattering problemJournal of Mathematical Physics, 1976
- Pseudopotentials and their applicationsPublished by Springer Nature ,1976