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Quasi-homoclinic solutions to a system of ODEs

Kaźmierczak B.

Archives of Mechanics

1999

Vol. 51, nr 1

105-120

This paper considers the problem of existence of "quasi-homoclinic" solution to a system of three first order ODEs containing a small parameter. These equations describe travelling wave solutions to a one-temperature model of laser-sustained plasma with absorption. This solution is homoclinic with respect to the first two variables. We use the methods of geometric singular perturbation theory to prove the existence of strictly homoclinic trajectory and then prove that it implies the existence of the desired solution.