扰动双扩散方程周期波的全局存在唯一性

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

数学季刊 ›› 2022, Vol. 37 ›› Issue (2): 124-131.doi: 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

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

收稿日期:2021-12-04 出版日期:2022-06-30 发布日期:2022-06-30
通讯作者: HUANG Wen-tao (1966-), male, native of Guilin, Guangxi, professor of Guangxi Normal University, engages in ordinary differential equation; E-mail: huangwentao@163.com
作者简介: 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.
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).

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

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:2021-12-04 Online:2022-06-30 Published:2022-06-30
Contact: HUANG Wen-tao (1966-), male, native of Guilin, Guangxi, professor of Guangxi Normal University, engages in ordinary differential equation; E-mail: huangwentao@163.com
About author: 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.
Supported by:
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).

摘要/Abstract

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

Abstract: 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.

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

中图分类号:

O175.12

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.

LIAO Xiao-zhao, HUANG Wen-tao, YANG Su-min. Global Existence and Uniqueness of Periodic Waves for a Perturbed Combined Double-Dispersive Equation[J]. Chinese Quarterly Journal of Mathematics, 2022, 37(2): 124-131.

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扰动双扩散方程周期波的全局存在唯一性

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

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