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

DOI10.1090/S0002-9947-07-04248-1zbMath1146.35069arXivmath/0501279OpenAlexW2003833708MaRDI QIDQ5437618

Feride Tiğlay

Publication date: 21 January 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501279

zbMATH Keywords

Sobolev spacesbi-Hamiltonian systemsperiodic initial value problemCauchy-Kowalevskaya type theoremsHamiltonian systems on groups of diffeomorphismsmodified Euler-Poisson equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) Cauchy-Kovalevskaya theorems (35A10) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Euler-Poisson-Darboux equations (35Q05)

Related Items

Mechanisms of Lagrangian analyticity in fluids ⋮ Nonlinear perturbations of evolution systems in scales of Banach spaces ⋮ Linear evolution equations in scales of Banach spaces ⋮ The Cauchy problem for a modified Euler-Poisson system in one dimension ⋮ Continuity properties of the solution map for the Euler-Poisson equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp estimates for analytic pseudodifferential operators and application to Cauchy problems
• Nonlinear evolution equations and analyticity. I
• Pseudodifferential operators and nonlinear PDE
• A note on a theorem of Nirenberg
• Soliton collisions in the ion acoustic plasma equations
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Topological methods in hydrodynamics
• Solitary wave interactions of the Euler-Poisson equations
• Analyticity of the Cauchy problem for an integrable evolution equation
• Remarks on the Euler equation
• The Cauchy problem for an integrable shallow-water equation
• Classical solutions of the periodic Camassa-Holm equation.
• Euler equations on homogeneous spaces and Virasoro orbits
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• Semidirect Products and Reduction in Mechanics
• The inverse problem for periodic potentials
• Multi-peakons and a theorem of Stieltjes
• Deformed Harry Dym and Hunter–Zheng equations
• An Abstract Nonlinear Cauchy-Kovalevska Theorem

This page was built for publication: The Cauchy problem and integrability of a modified Euler-Poisson equation