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Further results on the traveling wave solutions for an integrable equation. (English) Zbl 1266.37032
Summary: The objective of this paper is to extend some results of pioneers for the nonlinear equation $m_t = (1/2)(1/m^k)_{xxx} - (1/2)(1/m^k)_x$ introduced by Qiao. The equivalent relationship of the traveling wave solutions between the integrable equation and the generalized KdV equation is revealed. Moreover, when $k = -(p/q)$, $p \neq q$ and $p, q \in \Bbb Z^+$, we obtain some explicit traveling wave solutions by the bifurcation method of dynamical systems.
MSC:
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35C07Traveling wave solutions of PDE
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References:
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