In this paper we consider a chain of strings with fixed end points coupled by a nearest-neighbour interaction potential of exponential type, i.e. $$ \phi_{tt}^i-\phi_{xx}^i=\exp(\phi^{i+1}-\phi^i)-\exp(\phi^i-\phi^{i-1}),\quad i\in\Bbb Z,$$ $$0<x<\pi, t\in\Bbb R,$$ with periodicity conditions $ \phi^i(0,t)=\phi^i(\pi,t)=0$ for all $t$ and all $i$. We consider the case of `closed chains', i.e. $\phi^{i+N}=\phi^i$ for all $i\in\Bbb Z$ and some $N\in\Bbb N$, and look for solutions which are periodic in time. The existence of periodic solutions for the dual problem is proved in an Orlicz space setting

Mancini, G., Srikanth, P.N. (2005). On periodic motions of a two dimensional Toda type chain, 11, 72-87.

On periodic motions of a two dimensional Toda type chain

MANCINI, Giovanni;
2005-01-01

Abstract

In this paper we consider a chain of strings with fixed end points coupled by a nearest-neighbour interaction potential of exponential type, i.e. $$ \phi_{tt}^i-\phi_{xx}^i=\exp(\phi^{i+1}-\phi^i)-\exp(\phi^i-\phi^{i-1}),\quad i\in\Bbb Z,$$ $$0
2005
Mancini, G., Srikanth, P.N. (2005). On periodic motions of a two dimensional Toda type chain, 11, 72-87.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/269683
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