On periodic motions of a two dimensional Toda type chain
Gianni Mancini; P. N. Srikanth
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 11, Issue: 1, page 72-87
- ISSN: 1292-8119
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topMancini, Gianni, and Srikanth, P. N.. "On periodic motions of a two dimensional Toda type chain." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2010): 72-87. <http://eudml.org/doc/90757>.
@article{Mancini2010,
abstract = {
In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e.$$\left\\{\begin\{array\}\{l\}
\varphi^\{i\}\_\{tt\} - \varphi^\{i\}\_\{xx\} = \exp(\varphi^\{i+1\} -\varphi^\{i\}) - \exp( \varphi^\{i\} - \varphi\{i-1\} ) \quad 0<x<\pi, \quad t \in \rm I\hskip-1.8pt R, i \in Z\!\!\!Z\quad
(TC) \varphi^i (0,t) = \varphi^i (\pi,t) = 0 \quad \forall t, i.
\end\{array\}\right.$$
We consider the case of “closed chains" i.e.$ \varphi^\{i+N\} = \varphi^i \forall i \in Z\!\!\!Z$ and some $ N \in \{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.
},
author = {Mancini, Gianni, Srikanth, P. N.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Periodic; Toda type chain.; Toda chain; periodic solutions; mountain pass},
language = {eng},
month = {3},
number = {1},
pages = {72-87},
publisher = {EDP Sciences},
title = {On periodic motions of a two dimensional Toda type chain},
url = {http://eudml.org/doc/90757},
volume = {11},
year = {2010},
}
TY - JOUR
AU - Mancini, Gianni
AU - Srikanth, P. N.
TI - On periodic motions of a two dimensional Toda type chain
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 1
SP - 72
EP - 87
AB -
In this paper we consider a chain of strings with fixed end points coupled with nearest neighbour interaction potential of exponential type, i.e.$$\left\{\begin{array}{l}
\varphi^{i}_{tt} - \varphi^{i}_{xx} = \exp(\varphi^{i+1} -\varphi^{i}) - \exp( \varphi^{i} - \varphi{i-1} ) \quad 0<x<\pi, \quad t \in \rm I\hskip-1.8pt R, i \in Z\!\!\!Z\quad
(TC) \varphi^i (0,t) = \varphi^i (\pi,t) = 0 \quad \forall t, i.
\end{array}\right.$$
We consider the case of “closed chains" i.e.$ \varphi^{i+N} = \varphi^i \forall i \in Z\!\!\!Z$ and some $ N \in {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.
LA - eng
KW - Periodic; Toda type chain.; Toda chain; periodic solutions; mountain pass
UR - http://eudml.org/doc/90757
ER -
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