no. 1
On periodic motions of a two dimensional Toda type chain
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 72-87

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 tt i -ϕ xx i =exp(ϕ i+1 -ϕ i )-exp(ϕ i -ϕi-1)0<x<π,t∈ℝ,i∈ℤ(TC)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∈ℤ and some N∈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.

DOI : 10.1051/cocv:2004033
Classification : 58E30, 37J45
Keywords: periodic, Toda type chain 
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     title = {On periodic motions of a two dimensional {Toda} type chain},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {72--87},
     year = {2005},
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Mancini, Gianni; Srikanth, P. N. On periodic motions of a two dimensional Toda type chain. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 72-87. doi: 10.1051/cocv:2004033

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