A modified Calogero-Bogoyavlenskii-Schiff equation with variable coefficients and its non-isospectral Lax pair

Abstract

In this paper, we present a modified version with variable coefficients of the (2 + 1) dimensional Korteweg-de Vries, or Calogero-Bogoyavlenskii-Schiff equation, derived by applying the Painlevé test. Its Lax pair with a non-isospectral condition in (2 + 1) dimensions is also given. Moreover a transformation which links the form with variable coefficients to the canonical one is shown.