Singularity analysis in 2+1-dimensional generalization of the perturbation equations of the KdV hierarchy

Abstract

Using the perturbation expansion of multiple scales, a 2+1‐dimensional generalization of the perturbation equations of the KdV hierarchy is given. It is found that the system satisfies the Painlevé property and allows a set of Bäcklund transformations obtained by truncating the series expansions of the solutions about the singularity manifold. Copyright © 1999 John Wiley & Sons, Ltd.