Abstract
We investigated three-dimensional quantum systems with higher-order dispersion and nonlinear effects. The systems’ soliton dynamics is studied based on the (3+1)-dimensional higher-order nonlinear Schrödinger equation (NLSE). Based on the self-similar approach and the bright soliton-type solution of the (1+1)-dimensional NLSE, we derived the analytical bright soliton solution for the (3+1)-dimensional NLSE with higher-order dispersion and nonlinear effects, with the typical soliton feature pictorially demonstrated. Our study illustrates that a higher-dimensional medium with higher-order dispersion and nonlinear effects supports soliton behavior. This demonstrates the applicability of the theoretical treatment presented in this work.
Highlights
The nonlinear phenomenon is one of the most intriguing topics in current physical science subjects and is investigated heavily in theory and experimental aspects
As a one-dimensional setting is typical in numerous quantum systems for the specific integrability of the classical (1+1)dimensional nonlinear Schrödinger equation (NLSE) involved, numerous research work focuses on the main category of one-dimensional classical NLSE
II, we present the formulation of the fourth-order NLSE model with higher-order dispersion and nonlinear interaction effects and present relevant results on the typical analytical soliton solution of the corresponding (1+1)-dimensional higher-order NLSE
Summary
The nonlinear phenomenon is one of the most intriguing topics in current physical science subjects and is investigated heavily in theory and experimental aspects. Solitons are the typical nonlinear phenomena, which are generated through the balance between dispersion and nonlinear interaction effects of the systems under study. As soliton-type solutions are very typical and have the ultimate goal of analytical solution study in the NLSE and NLSE related model, prior work utilizing the Fexpansion method14,15,22 analytically solves the (1+1)-dimensional higher-order NLSE.
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