Multisoliton and general Wronskian solutions of a variable‐coefficient Korteweg–de Vries equation

Abstract

With the help of a suitable transformation of the potential function, a variable‐coefficient Korteweg–de Vries (vcKdV) equation is transformed into a quadrilinear form. This form is further transformed into a bilinear form by the introduction of an auxiliary variable. The multisoliton solution is obtained with the aid of the perturbation technique. Furthermore, using the Laplace expansion of the determinant and a set of conditions, we verify that the potential function expressed in the form of the Wronskian determinant satisfies the given bilinear equation. Lastly, some rational solutions of the vcKdV equation are also obtained.