Conservation laws, modulation instability and solitons interactions for a nonlinear Schrödinger equation with the sextic operators in an optical fiber

Abstract

Under investigation in this paper is a sextic nonlinear Schrodinger equation, which describes the pulses propagating along an optical fiber. Based on the symbolic computation, Lax pair and infinitely-many conservation laws are derived. Via the modiied Hirota method, bilinear forms and multi-soliton solutions are obtained. Propagation and interactions of the solitons are illustrated graphically: Initial position and velocity of the soliton are related to the coefficient of the sixth-order dispersion, while the amplitude of the soliton is not affected by it. Head-on, overtaking and oscillating interactions between the two solitons are displayed. Through the asymptotic analysis, interaction between the two solitons is proved to be elastic. Based on the linear stability analysis, the modulation instability condition for the soliton solutions is obtained.