Nonisospectral effects on generating localized waves

Abstract

In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media. The nonisospectral Korteweg–de Vries, modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the idea. Their solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.