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

B. Kaźmierczak

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

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B. Kaźmierczak Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

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 + Ï•(u)) = 0, where λ is an arbitrary polynomial in Ï• and is properly chosen. The results are used in a simple model of plasma sustained by a laser beam.

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

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