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Homoclinic orbits for the perturbed sine‐Gordon equation
Author(s) -
Shatah Jalal,
Zeng Chongchun
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200003)53:3<283::aid-cpa1>3.0.co;2-2
Subject(s) - homoclinic orbit , mathematics , perturbation (astronomy) , mathematical analysis , sine , orbit (dynamics) , fredholm integral equation , perturbation theory (quantum mechanics) , mathematical physics , integral equation , physics , geometry , bifurcation , quantum mechanics , engineering , nonlinear system , aerospace engineering
In this work, we study the persistence of a homoclinic orbit of the sine‐Gordon equation under diffusive and driven perturbations. An analytic perturbation method based on time‐dependent scattering theory, together with Fredholm theory, is used to establish persistence. The estimates are given in space‐time function spaces, with a certain time decay required for the existence of a homoclinic orbit. © 2000 John Wiley & Sons, Inc.