Mixed type Hermite-Padé approximation inspired by the Degasperis-Procesi equation

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...

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...

A study on Degasperis - Procesi equation by iterative methods

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...