具有克尔非线性定律的拉克什曼-波尔舍-丹尼尔方程的分岔分析和周期函数的单调性

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-05-03 DOI:10.1007/s12346-024-01042-8

Lin Lu, Xiaokai He, Aiyong Chen

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引用次数: 0

摘要

讨论了具有克尔非线性定律的拉克什曼-波尔齐安-丹尼尔方程周期函数的分岔和单调性。首先，通过行波变换，将 Lakshmanan-Porsezian-Daniel 方程还原为平面哈密顿系统，其哈密顿函数包含一个 6 次多项式。然后，我们给出了哈密顿系统的相位肖像，并利用动力系统的分岔方法构造了一些行波，包括暗波解、扭结解和反扭结解以及周期解。此外，我们还利用杨和曾（Bull Sci Math 133(6):555-557, 2009）提出的一些定理讨论了周期波解的周期函数单调性。最后，还介绍了一些数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity

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Bifurcations Analysis and Monotonicity of the Period Function of the Lakshmanan–Porsezian–Daniel Equation with Kerr Law of Nonlinearity

The bifurcations and monotonicity of the period function of the Lakshmanan–Porsezian–Daniel equation with Kerr law of nonlinearity are discussed. Firstly, by the traveling wave transformations, the Lakshmanan–Porsezian–Daniel equation is reduced to the planar Hamiltonian system whose Hamiltonian function includes a 6-th degree polynomial. Then we give the phase portraits of the Hamiltonian system, and some traveling waves including dark wave solutions, kink and anti-kink solutions and periodic solutions are constructed by using the bifurcation method of dynamical systems. Furthermore, we discuss the monotonicity of the period function of periodic wave solutions by using some Lemmas proposed by Yang and Zeng (Bull Sci Math 133(6):555-557, 2009). Finally, some numerical simulations are presented.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.