一般 N 分量非线性薛定谔方程的有理解和半有理解的动力学特性

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2024-09-27 DOI:10.1016/j.apm.2024.115726

Wei-Qi Peng

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引用次数: 0

摘要

我们研究了可积分的一般 N 分量非线性薛定谔方程。首先根据其拉克斯对构造了方程的达布变换。运用分离变量的思想，我们生成了具有非三维背景的 Lax 对方程的解。然后，我们详细推导出方程的有理向量解和半有理向量解。有理解是纯流氓波。半理性解代表不同类型的流氓波、呼吸波和孤子波的组合。此外，还给出了将半有理解还原为非混合呼吸波或第 n 次流氓波的约束条件。为了说明这些解的相应动态行为，我们分析了两分量和四分量的情况，结果表明与低分量系统相比，多分量系统表现出更丰富的现象和新颖的行为，同时也呈现出一些新奇的现象。

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Dynamics of rational and semi-rational solutions of the general N-component nonlinear Schrödinger equations

We investigate an integrable general N-component nonlinear Schrödinger equations. The Darboux-dressing transformation for the equations is firstly constructed according to its Lax pair. Applying the idea of separating variables, we generate the solutions of the Lax pair equations with a nontrivial background. Then we derive the rational and semi-rational vector solutions of the equations in detail. The rational solutions act as the pure rogue waves. The semi-rational solutions represent a combination of different types of rogue waves, breathers, and soliton waves. Moreover, a constraint condition is given for the semi-rational solutions being reduced to unmixed breather or nth-rogue waves. To illustrate the corresponding dynamic behaviors of these solutions, we analyze two-component and four-component cases, showing that the multi-component system exhibits richer phenomena and novel behaviors compared to lower-component systems, and also presenting some novel phenomena.

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.