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Lagrangian foliations and Lax equations

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Abstract

If X is a bihamiltonian vector field tangent to a foliation which is Lagrangian with respect to both symplectic structures, the dynamical system x=X(x) implies a ‘local Lax equation’ Ŀ=[L, B], but in canonical adapted coordinates, this equation reduces to the trivial equation Ŀ=0.

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  1. UER de Mathématiques, Université de Lille I, 59655, Villeneuve d'Ascq, France

    Yvette Kosmann-Schwarzbach

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  1. Yvette Kosmann-Schwarzbach
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Kosmann-Schwarzbach, Y. Lagrangian foliations and Lax equations. Lett Math Phys 9, 163–167 (1985). https://doi.org/10.1007/BF00400715

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  • DOI: https://doi.org/10.1007/BF00400715

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