Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

Journal Article · Sun Sep 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526841· OSTI ID:5344789

Weiss, J

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for the iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.

• Research Organization: Center for Studies of Nonlinear Dynamics, La Jolla Institute, 8950 Villa La Jolla Drive, Suite 2150, La Jolla, California 92037 and Institute for Pure and Applied Physical Science, University of California, San Diego, La Jolla, California 92093
• DOE Contract Number: AC03-81ER10923
• OSTI ID: 5344789
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BAECKLUND TRANSFORMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL MANIFOLDS
MODIFICATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
RECURSION RELATIONS
SERIES EXPANSION
SINGULARITY
TRANSFORMATIONS