Computational techniques for fluid dynamics: C.A.J. Fletcher, Springer Series in Computational Physics, Springer-Verlag, Heidelberg, 2nd ed. 1991. Two volumes; 425 and 515 pages, respectively. Softcover price DM 65.00 and DM 75.00, respectively. ISBN 3 540 53058 4 and 3 540 53601 9.

Abstract

This paper addresses the cubic nonlinear Schrödinger equation with a bounded potential (CNLSE) which describes optical solitary waves propagation properties in optical fiber. A gray optical soliton solution of this equation is retrieved for the first time by adopting an appropriate solitary wave ansatz which play a vital role in understanding various physical phenomena in nonlinear systems. The integration lead to a constraint condition on the solitary wave parameters which must hold for the soliton to exist. We studied the conservation laws (Cls) of the CNLSE by analyzing a system of partial differential equations (PDEs) obtained by transforming the equation into real and imaginary components. The multiplier approach is employed to retrieve the conservation laws. Moreover, the modulation instability (MI) analysis of the model is studied by employing the linear-stability analysis and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE.