Abstract
In this study, we investigate the typical systems modeled by the (3 + 1)-dimensional as well as (1 + 1)-dimensional Schrödinger equations incorporating third-order dispersion effects, higher-order scattering effects, and cubic–fifth–seventh degree nonlinear interactions. We use the F-expansion method and the self-similar method to solve the higher-order Schrödinger equation for one-dimensional and three-dimensional settings, respectively, identifying typical bright soliton solutions under appropriate system settings. The bright soliton features are demonstrated analytically in regions around the soliton peak region. Pictorial bright soliton features are demonstrated for the three-dimensional setting as well as one-dimensional setting. Our work shows the applicability of the theoretical treatment utilized in studying bright soliton dynamics for systems with third-order dispersion and seventh degree nonlinearity.
Highlights
Due to the balance of the dispersion effect and scattering effect,1–3 solitons exhibit robust stability in the process of propagation and interaction.4 It is an extremely important phenomenon in modern physics, which has attracted extensive attention in theoretical and experimental research due to its unique properties
We study the (3 + 1)-dimensional as well as (1 + 1)-dimensional higher-order Schrödinger equations incorporating the third-order dispersion effect and the cubic–fifth–seventh degree nonlinear interaction,16 and we use the F-expansion17,18 method and the self-similar method19–21 to solve the threedimensional as well as one-dimensional higher-order nonlinear Schrödinger equation (NLSE) under appropriate parametric settings
We first identify the bright soliton solutions by deriving the one-dimensional solution of the bright soliton type, the three-dimensional bright soliton solution is identified, and we derive the key characteristics of bright solitons around the location of the soliton peak, demonstrating typical bright soliton features
Summary
Due to the balance of the dispersion effect and scattering effect, solitons exhibit robust stability in the process of propagation and interaction. It is an extremely important phenomenon in modern physics, which has attracted extensive attention in theoretical and experimental research due to its unique properties. Due to the balance of the dispersion effect and scattering effect, solitons exhibit robust stability in the process of propagation and interaction.4 It is an extremely important phenomenon in modern physics, which has attracted extensive attention in theoretical and experimental research due to its unique properties. We study the (3 + 1)-dimensional as well as (1 + 1)-dimensional higher-order Schrödinger equations incorporating the third-order dispersion effect and the cubic–fifth–seventh degree nonlinear interaction, and we use the F-expansion method and the self-similar method to solve the threedimensional as well as one-dimensional higher-order NLSE under appropriate parametric settings.
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