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On periodic motions of a two dimensional Toda type chain

Gianni ManciniP. N. Srikanth — 2005

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e. ϕ t t i - ϕ x x i = exp ( ϕ i + 1 - ϕ i ) - exp ( ϕ i - ϕ i - 1 ) 0 < x < π , t , i ( T C ) ϕ i ( 0 , t ) = ϕ i ( π , t ) = 0 t , i . We consider the case of “closed chains” i.e. ϕ i + N = ϕ i i and some N and look for solutions which are peirodic in time. The existence of periodic solutions for the dual problem is proved in Orlicz space setting.

On periodic motions of a two dimensional Toda type chain

Gianni ManciniP. N. Srikanth — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, ϕ t t i - ϕ x x i = exp ( ϕ i + 1 - ϕ i ) - exp ( ϕ i - ϕ i - 1 ) 0 < x < π , t I R , i Z Z ( TC ) ϕ i ( 0 , t ) = ϕ i ( π , t ) = 0 t , i . We consider the case of “closed chains" ϕ i + N = ϕ i i Z Z and some N I N and look for solutions which are peirodic in time. The existence of periodic solutions for the dual problem is proved in Orlicz space setting.

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