منابع مشابه
Degasperis–Procesi peakons and the discrete cubic string
We use an inverse scattering approach to study multi-peakon solutions of the Degasperis–Procesi (DP) equation, an integrable PDE similar to the Camassa–Holm shallow water equation. The spectral problem associated to the DP equation is equivalent under a change of variables to what we call the cubic string problem, which is a third order non-selfadjoint generalization of the well-known equation ...
متن کامل1 99 5 A discrete time peakons lattice
A discretization of the peakons lattice is introduced, belonging to the same hierarchy as the continuous–time system. The construction examplifies the general scheme for integrable discretization of systems on Lie algebras with r–matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flow...
متن کاملRotating concentric circular peakons
We study circularly symmetric solution behaviour of invariant manifolds of singular solutions of the partial differential equation EPDiff for geodesic flow of a pressureless fluid whose kinetic energy is the H 1 norm of the fluid velocity. These singular solutions describe interaction dynamics on lower-dimensional support sets, for example, curves, or filaments, of momentum in the plane. The 2 ...
متن کاملPeakons and Cauchy Biorthogonal Polynomials
Peakons are non-smooth soliton solutions appearing in certain nonlinear partial differential equations, most notably the Camassa-Holm equation and the Degasperis-Procesi equation. In the latter case the construction of peakons leads to a new class of biorthogonal polynomials. The present paper is the first in the series of papers aimed to establish a general framework in which to study such pol...
متن کاملIntegrable and non-integrable equations with peakons
We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new integrable equation first isolated by Degasperis and Procesi. A Lagrangian and Hamiltonian formulation is presented for the whole family of equations, and we discuss how this fits into a bi-Hamiltonian framework in the integrable cases. The Hamilton...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2005
ISSN: 0167-2789
DOI: 10.1016/j.physd.2005.05.019