FORMULATION AND SOLUTION OF TIME-FRACTIONAL DEGASPERIS-PROCESI EQUATION VIA VARIATIONAL METHODS

Exact Traveling Wave Solution of Degasperis-Procesi Equation

In this paper, exact traveling wave solution of Degasperis–Procesi equation can be investigated via the first-integral method. By using the first-integral method which is based on the ring theory of commutative algebra, We construct exact traveling wave solution for Degasperis–Procesi equation , and the obtained solution agrees well with the previously known result.

A study on Degasperis - Procesi equation by iterative methods

Time-fractional Klein-Gordon equation: formulation and solution using variational methods

This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange variational technique in the Riesz derivative sense and derives an approximate solitary wave solution. Our results witness that He’s variational iteration method was very efficient and powerful technique in finding the solution of the proposed equation. The basic idea described in this paper is...

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...