Abstract: We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelling-wave solutions with unit velocity (in dimensionless units). For $|\gamma|$ not larger than 1 we find families of solutions that are all (except the obvious constant one) manifestly unstable, whereas for $|\gamma|>1$ we find families of stable solutions describing each an array of evenly spaced kinks.

Some explicit travelling-wave solutions of a perturbed sine-Gordon equation / Fiore, Gaetano. - STAMPA. - (2008), pp. 281-288. (Intervento presentato al convegno ``Mathematical Physics Models and Engineering Sciences'' tenutosi a Napoli nel 22-23 giugno 2006).

Some explicit travelling-wave solutions of a perturbed sine-Gordon equation

FIORE, GAETANO
2008

Abstract

Abstract: We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative term, and the equation is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. We determine all travelling-wave solutions with unit velocity (in dimensionless units). For $|\gamma|$ not larger than 1 we find families of solutions that are all (except the obvious constant one) manifestly unstable, whereas for $|\gamma|>1$ we find families of stable solutions describing each an array of evenly spaced kinks.
2008
9788820740573
Some explicit travelling-wave solutions of a perturbed sine-Gordon equation / Fiore, Gaetano. - STAMPA. - (2008), pp. 281-288. (Intervento presentato al convegno ``Mathematical Physics Models and Engineering Sciences'' tenutosi a Napoli nel 22-23 giugno 2006).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/118477
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