Bright solitons for the coupled cubic-quintic non-linear Schrödinger equations

Abstract

In this paper, we investigate the coupled cubic-quintic non-linear Schrodinger equations, which describe the effects of quintic non-linearity on the ultra-short optical-pulse propagation in the non-Kerr medium. Bi-linear forms, bright one- and two-soliton solutions are obtained with Hirota method and symbolic computation. Via the asymptotic analysis, we find that the bright two solitons keep their original amplitudes, widths and velocities invariant after each collision except for the phase shifts. By virtue of the graphical analysis, head-on and overtaking collisions between the bright two solitons are presented. Bound-state soliton can also be observed with the breather-like structures.