On periodic motions of a two dimensional Toda type chain

Mancini, Gianni; Srikanth, P. N.

doi:10.1051/cocv:2004033

Geodesic

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On periodic motions of a two dimensional Toda type chain

Mancini, Gianni ; Srikanth, P. N.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 72-87

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Résumé

In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e.

\{\begin{matrix} ϕ_{t t}^{i} - ϕ_{x x}^{i} = exp (ϕ^{i + 1} - ϕ^{i}) - exp (ϕ^{i} - ϕ i - 1) & 0 < x < π, t \in ℝ, i \in ℤ (T C) \\ ϕ^{i} (0, t) = ϕ^{i} (π, t) = 0 & \forall t, i . \end{matrix}

We consider the case of “closed chains” i.e.

ϕ^{i + N} = ϕ^{i} \forall i \in ℤ

and some

N \in 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.

MR Zbl

DOI : 10.1051/cocv:2004033

Classification : 58E30, 37J45
Keywords: periodic, Toda type chain

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     author = {Mancini, Gianni and Srikanth, P. N.},
     title = {On periodic motions of a two dimensional {Toda} type chain},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {72--87},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {1},
     year = {2005},
     doi = {10.1051/cocv:2004033},
     mrnumber = {2110614},
     zbl = {1096.37049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004033/}
}

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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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