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Heteroclinic Solutions for a System of Strongly Coupled ODEs
Author(s) -
Kazmierczak B.,
Peradzynski Z.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199604)19:6<451::aid-mma770>3.0.co;2-3
Subject(s) - ode , mathematics , heteroclinic orbit , heteroclinic bifurcation , heteroclinic cycle , perturbation (astronomy) , implicit function theorem , mathematical analysis , traveling wave , initial value problem , nonlinear system , bifurcation , physics , period doubling bifurcation , quantum mechanics , homoclinic orbit
We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non‐linear second‐order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.