Abstract
Objective:The generalized Schrödinger equation for description of embedded solitons is considered. The objective of this paper is to find the analytical solutions of the equation. Method:The Cauchy problem for studied partial differential equation cannot be solved by the inverse scattering transform and some exact solutions of equation are looked for using the traveling wave reduction. The system of equations corresponding to the partial differential equation is analyzed. Method of simplest equations is used to find exact solutions of overdetermined system of equations. Results:Exact solutions of the studied equation in the form of periodic and solitary waves are found for one of the equations for description of embedded solitons.
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