A study on Degasperis - Procesi equation by iterative methods

a study on degasperis - procesi equation by iterative methods

A Note on the Degasperis-Procesi Equation

Indeed [1, 13, 15], both equations are bi-Hamiltonian and have an associated isospectral problem. Therefore they are both formally integrable (the integrability of (1.2) by means of the scattering/inverse scattering approach is discussed in [5, 9, 19]). Also, both equations admit exact peaked solitary wave solutions which have to be understood as weak solutions [10, 8, 22]. Moreover, using Kato...

Fourier Spectral Methods for Degasperis-Procesi Equation with Discontinuous Solutions

In this paper, we develop, analyze and test the Fourier spectral methods for solving the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The L2 stability is obtained for general numerical solutions of the Fourier Galerkin method and Fourier collocation (pseudospectral) method. By applying the Gegenbauer ...

Cusp solitons of the Degasperis-Procesi equation

In this paper, we present cusp solitons for the Degasperis-Procesi (DP) equation under the inhomogeneous boundary condition lim|x|→∞ u= A, where A is a non-zero constant. Through mathematical analysis, a stationary cusp soliton is presented in an explicit form of u(x, t) = √ 1− e−2|x| ∈ W 1,1 loc , but / ∈ H1 loc, while most cusp solitons are expressed in an implicit form in the space ofW 1,1 l...

The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of b-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Proces...

On the Well-posedness of the Degasperis-procesi Equation

We investigate well-posedness in classes of discontinuous functions for the nonlinear and third order dispersive Degasperis-Procesi equation (DP) ∂tu− ∂ txxu + 4u∂xu = 3∂xu∂ xxu + u∂ xxxu. This equation can be regarded as a model for shallow-water dynamics and its asymptotic accuracy is the same as for the Camassa-Holm equation (one order more accurate than the KdV equation). We prove existence...