Some geometric investigations on the Degasperis-Procesi shallow water equation

DOI10.1016/j.wavemoti.2009.06.005zbMath1231.76044OpenAlexW2081186844MaRDI QIDQ661744

Boris Kolev

Publication date: 11 February 2012

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.wavemoti.2009.06.005

zbMATH Keywords

geodesic flowCamassa-Holm equationDegasperis-Procesi equationdiffeomorphism group of the circle

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65)

Related Items (13)

RESTRICTIONS ON THE GEOMETRY OF THE PERIODIC VORTICITY EQUATION ⋮ Geometric Aspects of the Periodic μ-Degasperis-Procesi Equation ⋮ The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations ⋮ Curvature computations for a two-component Camassa-Holm equation with vorticity ⋮ Limit behavior of the global solutions to the Degasperis-Procesi-type equation ⋮ One-dimensional weakly nonlinear model equations for Rossby waves ⋮ The Degasperis-Procesi equation as a non-metric Euler equation ⋮ The Periodic μ-b-Equation and Euler Equations on the Circle ⋮ On the global boundary stabilization of the Camassa-Holm equation ⋮ Non-uniform dependence on initial data for the periodic Degasperis-Procesi equation ⋮ Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach ⋮ A view of the peakon world through the lens of approximation theory ⋮ The periodic b-equation and Euler equations on the circle

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