Some explicit forrnulae for heteroclinic solutions to scalar second order ordinary differential equations

Abstract

We derive some explicit formulae for heteroclinic pairs for scalar ordinary differential equations of the form u" + vλ(u)u' - su(u - a)(u - 1)(1 + ϕ(u)) = 0, where λ is an arbitrary polynomial in ϕ and is properly chosen. The results are used in a simple model of plasma sustained by a laser beam.