The connection between the Painleve property for partial differential equations, proposed by J. Weiss et al. and R. Hirota's method for calculating N-soliton solutions is investigated for a variety of equations including the nonlinear Schroedinger and mKdV equations. Those equations which do not possess the Painleve property are easily seen not to have self-truncating Hirota expansions. The Backlund transformations derived from the Painleve analysis and those determined by Hirota's method are shown to be directly related. This provides a simple route for demonstrating the connection between the singular manifolds used in the Painleve analysis and the eigenfunctions of the AKNS inverse scattering transform.
ASJC Scopus subject areas
- Applied Mathematics