The quasi-Gramian solution of a non-commutative extension of the higher-order nonlinear Schrödinger equation

IF 2.4 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Communications in Theoretical Physics Pub Date : 2024-03-06 DOI:10.1088/1572-9494/ad244f

H W A Riaz, J Lin

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引用次数: 0

Abstract

The nonlinear Schrödinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the higher-order NLS equation. We treat real or complex-valued functions, such as g ₁ = g ₁(x, t) and g ₂ = g ₂(x, t) as non-commutative, and employ the Lax pair associated with the evolution equation, as in the commutation case. We derive the quasi-Gramian solution of the system by employing a binary Darboux transformation. The soliton solutions are presented explicitly within the framework of quasideterminants. To visually understand the dynamics and solutions in the given example, we also provide simulations illustrating the associated profiles. Moreover, the solution can be used to study the stability of plane waves and to understand the generation of periodic patterns within the context of modulational instability.

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高阶非线性薛定谔方程非交换扩展的准伽马解

非线性薛定谔（NLS）方程包含高阶色散项，被广泛应用于各种物理现象的理论分析。在本研究中，我们探讨了高阶 NLS 方程的非交换扩展。我们将实值或复值函数，如 g1 = g1(x, t) 和 g2 = g2(x, t) 视为非交换函数，并采用与演化方程相关的拉克斯对，就像在交换情况下一样。我们通过二元达尔布克斯变换推导出系统的准格拉玛解。孤子解在准决定子框架内明确呈现。为了直观地理解给定例子中的动力学和解，我们还提供了相关剖面的模拟图。此外，该解法还可用于研究平面波的稳定性，并在调制不稳定性的背景下理解周期模式的产生。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Theoretical Physics 物理-物理：综合

CiteScore

5.20

自引率

3.20%

发文量

6110

审稿时长

4.2 months

期刊介绍： Communications in Theoretical Physics is devoted to reporting important new developments in the area of theoretical physics. Papers cover the fields of: mathematical physics quantum physics and quantum information particle physics and quantum field theory nuclear physics gravitation theory, astrophysics and cosmology atomic, molecular, optics (AMO) and plasma physics, chemical physics statistical physics, soft matter and biophysics condensed matter theory others Certain new interdisciplinary subjects are also incorporated.