Similarity transformations and exact solutions of the generalized ( \begin{document}$ n+1 $\end{document} )-dimensional Schrödinger equation with ( \begin{document}$ 2 m+1 $\end{document} )th order nonlinear terms and spatiotemporally varying coefficients
Year: 2025
Type: article
Abstract: Schrödinger-type equations represent a fundamentally important class of differential equations. Research on high-dimensional variable-coefficient Schrödinger-type equations as important theoretical and practical value, providing critical insights into the dynamics of complex wave phenomena. In this paper, we employ similarity transformations to derive a novel class of soliton solutions for the (n + 1)-dimensional (2m + 1)th-order variable-coefficient nonlinear Schrödinger equation. By extending similarity transformations from lower-dimensional to higher dimensionnal equations, we establish the intrinsic relationships among the equation’s coefficients. Furthermore, utilizing the solutions of the stationary Schrödinger equation and using the balancing-coefficient method, we construct both bright and dark soliton solutions for the (n + 1)-dimensional (2m + 1)th-order variable-coefficient nonlinear Schrödinger equation. Finally, for specific cases, we present graphical representations of the bright and dark soliton solutions and conduct a systematic analysis of their spatial structures and propagation characteristics. Our results indicate that bright solitons exhibit a single-peak structure, while dark solitons form trough-like profiles, further confirming the stability of soliton wave propagation.
Source: Acta Physica Sinica
Authors: Gangwei WANG, Zixuan TAN
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408898744