By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equation m(t) + c(0)u(x) + um(x) + 2mu(x) = -yu(xxx) with m = u - alpha(2)u(xx), alpha not equal 0, co, gamma are constant, whi...
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By using the bifurcation theory of planar dynamical systems to a generalized Camassa-Holm equation m(t) + c(0)u(x) + um(x) + 2mu(x) = -yu(xxx) with m = u - alpha(2)u(xx), alpha not equal 0, co, gamma are constant, which is called CH-r equation, the existence of peakons and periodic cusp wave solutions is obtained. The analytic expressions of the peakons and periodic cusp wave solutions are given and numerical simulation results show the consistence with the theoretical analysis at the same time. (c) 2005 Elsevier Ltd. All rights reserved.
In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and non-smooth traveling wave solutions of the generalized Degasperis-Procesi equation ut-uxxt+4umux-3uxuxx+uuxxx. with m...
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In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and non-smooth traveling wave solutions of the generalized Degasperis-Procesi equation ut-uxxt+4umux-3uxuxx+uuxxx. with m∈N which is the well-known Degasperis-Procesi equation when m=1. We will show in this paper that the GDP equation also has the similar topological bifurcation phase portraits as
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