Existence of multi-hump generalized homoclinic solutions for a class of reversible systems  

作　　者：Shengfu Deng Yan Zhou Jinsen Zhuang 

机构地区：[1]School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China

出　　处：《Science China Mathematics》2025年第2期299-338,共40页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant No.12171171);Natural Science Foundation of Fujian Province of China(Grant Nos.2022J01303 and 2023J01121);the Scientific Research Funds of Huaqiao University。

摘　　要：In this paper,we investigate a class of reversible dynamical systems in four dimensions.The spectrums of their linear operators at the equilibria are assumed to have a pair of positive and negative real eigenvalues and a pair of purely imaginary eigenvalues for the small parameterμ>0,where these two real eigenvalues bifurcate from a double eigenvalue 0 forμ=0.It has been shown that this class of systems owns a generalized homoclinic solution with one hump at the center(a homoclinic solution exponentially approaching a periodic solution with a small amplitude).This paper gives a rigorous existence proof of two-hump solutions.These two humps are far away and are glued by the small oscillations in the middle if some appropriate free constants are activated.The obtained results are also applied to some classical systems.The ideas here may be used to study the existence of 2^(k)-hump solutions.

关 键 词：homoclinic solutions multi-hump periodic solutions REVERSIBILITY 

分 类 号：O17[理学—数学]