Nonautonomous solitons of the generalized complex mKdV equation in external potentials

Abstract

The generalized nonautonomous complex modified Korteweg–de Vries (mKdV) equation with external potentials is introduced in the framework of the nonisospectral generalization of the Inverse Scattering Transform method with associated spectral parameter varying in accordance with the Riccati equation. Nonautonomous accelerating and self-compressing mKdV solitons exist only if the varying dispersion, nonlinearity, and the external linear, parabolic, and cubic potentials satisfy to the conditions of the exact integrability of the introduced model.