74 research outputs found
Soliton, kink and antikink solutions of a 2-component of the Degasperis-Procesi equation
In this paper, we employ the bifurcation theory of planar dynamical systems
to investigate the traveling wave solutions of a 2-component of the
Degasperis-Procesi equation. The expressions for smooth soliton, kink and
antikink solutions are obtained.Comment: 16 pages, 18 figure
Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation
We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations of un+1(x,t) which is converged to u(x,t) are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximation u0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically
Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal
We investigate the traveling solitary wave solutions of the generalized Camassa-Holm equation ut - uxxt + 3u2ux=2uxuxx + uuxxx on the nonzero constant pedestal limξ→±∞uξ=A. Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation. Some exact explicit solutions are obtained. We show some graphs to explain our these solutions
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