具有[公式省略]对称势的非局部Gross-Pitaevskii方程中的非自治有理孤子束缚态和动力学

IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
Haotian Wang , Fenghua Qi , Wenjun Liu
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引用次数: 0

摘要

本文研究了一类具有非局部非线性效应的可积Gross-Pitaevskii方程,该方程由一个非局部非线性Schrödinger方程和一个外部势函数组成。采用广义达布变换直接求解该方程。我们得到了在束缚态下暗孤子和反暗孤子共存的理性孤子,并通过数值模拟验证了这些解的正确性和鲁棒性。讨论了非局部效应和外部势对有理型孤子解的影响。结果表明,这些解的动力学行为是新颖的,不同于局部Gross-Pitaevskii方程和非局部非线性Schrödinger方程的动力学行为,为光学实验中各种孤子束缚态的实现提供了一定的帮助和指导。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-autonomous rational soliton bound states and dynamics in the nonlocal Gross–Pitaevskii equation with a PT-symmetric potential
This paper investigates an integrable Gross–Pitaevskii equation with nonlocal nonlinear effects, which consists of a nonlocal nonlinear Schrödinger equation adding an external potential function. The generalized Darboux transformation is used to solve this equation directly. We obtain rational solitons that exhibit the coexistence of dark and anti-dark solitons in bound states, and numerical simulations verify the correctness and robustness of these solutions. The influence of nonlocal effects and external potentials on the solutions of rational-type solitons is discussed. Results demonstrated that the dynamical behaviors of these solutions are novel and distinct from those of the local Gross–Pitaevskii equation and nonlocal nonlinear Schrödinger equation, providing some help and guidance for the realization of various soliton bound states in optical experiments.
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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