In this paper, the cubic-quartic nonlinear Schrodinger and resonant nonlinear Schrodinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the m + G ′ G improved expansion method and the exp − φ ξ expansion method are utilized to construct some novel solutions of the governing equations. The obtained optical soliton solutions are presented graphically to clarify their physical parameters. Moreover, to verify the existence solutions, the constraint conditions are utilized.

Optical Soliton Solutions of the Cubic-Quartic Nonlinear Schrödinger and Resonant Nonlinear Schrödinger Equation with the Parabolic Law

Traveling wave solutions of the generalized nonlinear Schrödinger equation with cubic-quintic nonlinearity

A nonlinear fourth-order differential equation with arbitrary refractive index for description of the pulse propagation in an optical fiber is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for solutions of the equation using the traveling wave reduction. We present a novel method for finding soliton solutions of nonlinear evolution equations. The essence of this method is based on the hypothesis about the possible type of an auxiliary equation with an already known solution. This new auxiliary equation is used as a basic equation to look for soliton solutions of the original equation. We have found three forms of soliton solutions of the equation at some constraints on parameters of the equation.

Lingfei Li

Papers

New exact solutions to the high dispersive cubic–quintic nonlinear Schrödinger equation