Embedded Solitons of the Generalized Nonlinear Schrödinger Equation with High Dispersion
Regular and Chaotic Dynamics, ISSN: 1468-4845, Vol: 27, Issue: 6, Page: 680-696
2022
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Article Description
The family of generalized Schrödinger equations is considered with the Kerr nonlinearity. The partial differential equations are not integrable by the inverse scattering transform and new solutions of this family are sought taking into account the traveling wave reduction. The compatibility of the overdetermined system of equations is analyzed and constraints for parameters of equations are obtained.A modification of the simplest equation method for finding embedded solitons is presented.A block diagram for finding a solution to the nonlinear ordinary differential equation isgiven. The theorem on the existence of bright solitons for differential equations of any orderwith Kerr nonlinearity of the family considered is proved. Exact solutions of embedded solitonsdescribed by fourth-, sixth-, eighth and tenth-order equations are found using the modified algorithm of the simplest equation method. New solutions for embedded solitons of generalized nonlinear Schrödinger equations with several extremes are obtained.
Bibliographic Details
Pleiades Publishing Ltd
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