Solitary wave and periodic solutions of nonlinear Schrödinger equation including higher order dispersions

Abstract

The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi functions are obtained for the nonlinear Schrödinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The approach is based on the reduction of the generalized nonlinear Schrödinger equation to an ordinary nonlinear differential equation. The periodic solutions obtained form one-parameter family which depend on an integration constant p. The solitary wave solution with sech shape is the limiting case of this family with p=0. The solutions obtained describe also a train of soliton-like pulses with sech shape. It is shown that the bounded periodic solutions arise for special domains of integration constant