Title

Exact Conditions For Existence Of Homoclinic Orbits In The Fifth-Order Kdv Model

Abstract

We consider homoclinic orbits in the fourth-order equation v(iv) + (1 - ε2)v″ - ε2v ≤ v2 + γ(2vv″ + v′2), where . Numerical computations [CG97, C01] show that homoclinic orbits exist on certain curves γ(ε) in the parameter plane (γ, ε). We study the dependence γ(ε) in the limit ε → 0 and prove that a curve γ(ε) passes through the point (γ0, 0) only if s(γ0) ≤ 0, where s(γ) denotes the Stokes constant for the truncated equation (with ε ≤ 0). The additional condition s′(γ0) ≠ 0 guarantees the existence of a unique curve γ(ε) passing through the point (γ0, 0). Every homoclinic orbit is proved to be single-humped for sufficiently small ε. © 2006 IOP Publishing Ltd and London Mathematical Society.

Publication Date

10-1-2006

Publication Title

Nonlinearity

Volume

19

Issue

10

Number of Pages

2277-2312

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0951-7715/19/10/003

Socpus ID

33748880691 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33748880691

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