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 Poincaré bifurcation theory. Simulation is carried out to verify the theoretical result.
作者
LIAO Xiao-zhao
HUANG Wen-tao
YANG Su-min
廖笑照;黄文韬;杨素敏(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China;School of Public Administration,Guangxi Technological College of Machinery and Electrcity,Nanning 530007,China)
基金
Supported by the National Natural Science Foundation of China(Grant No.12061016)
the Applied Mathematics Center of Guangxi
Foundation of Guangxi Technological College of Machinery and Electrcity(Grant No.2021YKYZ010).
作者简介
LIAO Xiao-zhao(1996-),male,native of Yueyang,Hunan,postgraduate of Guangxi Normal University,engages in ordinary di erential equation;Corresponding author:HUANG Wen-tao(1966-),male,native of Guilin,Guangxi,professor of Guangxi Normal University,engages in ordinary di erential equation,huangwentao@163.com;YANG Su-min(1984-),female,native of Fugou,Henan,lecturer of Guangxi Technological College of Machinery and Electrcity,engages in dynamical systems.
