扰动双扩散方程周期波的全局存在唯一性

廖笑照, 黄文韬, 杨素敏

doi:10.13371/j.cnki.chin.q.j.m.2022.02.002

数学季刊 >

2022 , Vol. 37 >Issue 2: 124 - 131

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.02.002

扰动双扩散方程周期波的全局存在唯一性

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1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China;
2. School of Public Administration, Guangxi Technological College of Machinery and Electrcity,
Nanning 530007, China

LIAO Xiao-zhao (1996-), male, native of Yueyang, Hunan, postgraduate of Guangxi Normal University, engages in ordinary differential equation; HUANG Wen-tao (1966-), male, native of Guilin, Guangxi, professor of Guangxi Normal University, engages in ordinary differential equation; YANG Su-min (1984-), female, native of Fugou, Henan, lecturer of Guangxi Technological College of Machinery and Electrcity, engages in dynamical systems.

收稿日期: 2021-12-04

网络出版日期: 2022-06-30

基金资助

Supported by the National Natural Science Foundation of China (Grant No. 12061016) and the Applied Mathematics Center of Guangxi; Foundation of Guangxi Technological College of Machinery and Electrcity (Grant No. 2021YKYZ010).

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Global Existence and Uniqueness of Periodic Waves for a Perturbed Combined Double-Dispersive Equation

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1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China;
2. School of Public Administration, Guangxi Technological College of Machinery and Electrcity,
Nanning 530007, China

Received date: 2021-12-04

Online published: 2022-06-30

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摘要

In this paper, we study the periodic wave propagation phenomenon in elastic waveguides modeled by a combined double-dispersive partial differential equation (PDE). The traveling wave ansazt transforms the PDE model into a perturbed integrable ordinary differential equation (ODE). The global bifurcation theory is applied for the perturbed ODE model to establish the existence and uniqueness of the limit cycle, which corresponds
the periodic traveling wave for the PDE model. The main tool is the Abelian integral taken from Poincar´ e bifurcation theory. Simulation is carried out to verify the theoretical result.

关键词： Combined double-dispersive PDE; Abelian integral; Limit cycle; Hamiltonian function; Periodic wave

本文引用格式

廖笑照, 黄文韬, 杨素敏 . 扰动双扩散方程周期波的全局存在唯一性[J]. 数学季刊, 2022 , 37(2) : 124 -131 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.002

Abstract

Key words： Combined double-dispersive PDE; Abelian integral; Limit cycle; Hamiltonian function; Periodic wave

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