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The Cauchy problem and integrability of a modified Euler-Poisson equation

Authors:	Feride Tiglay

Affiliation:	Department of Mathematics, University of New Orleans, Lake Front, New Orleans, Louisiana 70148

Abstract:	We prove that the periodic initial value problem for a modified Euler-Poisson equation is well-posed for initial data in $H^{s}(mathbb{T}^{m})$ when . We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem. After presenting a formal derivation of the equation on the semidirect product space $mathrm{Diff} ltimes C^{infty}(mathbb{T})$ as a Hamiltonian equation, we concentrate on one space dimension () and show that the equation is bihamiltonian.

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