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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
