TY - JOUR
T1 - High order Melnikov method
T2 - Theory and application
AU - Chen, Fengjuan
AU - Wang, Qiu-Dong
PY - 2019/1/1
Y1 - 2019/1/1
N2 -
Let D(t
0
,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t
0
,ε) as a formal power series in ε as D(t
0
,ε)=E
0
(t
0
)+εE
1
(t
0
)+⋯+ε
n
E
n
(t
0
)+⋯. In this paper we derive an explicit integral formula for E
1
(t
0
). We also evaluate E
1
(t
0
) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
AB -
Let D(t
0
,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t
0
,ε) as a formal power series in ε as D(t
0
,ε)=E
0
(t
0
)+εE
1
(t
0
)+⋯+ε
n
E
n
(t
0
)+⋯. In this paper we derive an explicit integral formula for E
1
(t
0
). We also evaluate E
1
(t
0
) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
KW - High order Melnikov method
KW - Homoclinic intersection
KW - Time periodic equation
UR - http://www.scopus.com/inward/record.url?scp=85061381971&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061381971&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2019.02.003
DO - 10.1016/j.jde.2019.02.003
M3 - Article
AN - SCOPUS:85061381971
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
ER -