New solitons for the Hirota equation and generalized higher-order nonlinear Schrödinger equation with variable coefficients

In this paper, multisoliton solutions of the Hirota equation with variable coefficients are obtained by the Darboux transformation based on the Ablowitz–Kaup–Newell–Segur technology. As an example, we discuss the evolutional behaviour of a two-soliton solution in a soliton control fibre system. The results reveal that one may control the interaction between the pulses by choosing the third-order dispersion parameters d 4 and h appropriately. Meanwhile, more generalized forms of bright soliton and dark soliton solutions of generalized higher order nonlinear Schrödinger equations (GHONLSE) with variable coefficients are obtained by the extended tanh-function method. Moreover, new bright and dark combined solitary wave, kink solitary wave and M-shaped solitary wave to GHONLSE with variable coefficients are firstly reported in this paper. Especially, the term proportional to α 1 resulting from the group velocity decides the group velocity and the phase shift of these new solitary waves.