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Traveling-wave solutions and the coupled Korteweg-de Vries equation. (English) Zbl 0614.35080
This short paper deals with coupled nonlinear wave equations, involving two dependent variables u(x,t) and v(x,t), originally proposed by M. Ito [Phys. Lett. A 91, 335-338 (1982)] and later generalized by S. Kawamoto [J. Phys. Soc. Jen. 53, 1203-1205 (1984)]. The authors study their traveling-wave solutions by introducing a stream function ψ. It was shown that if one of the solutions is a function of (x-ct), the other must exhibit the same dependence of variables. Furthermore, inclusion of cubic nonlinear terms was considered, and corresponding solutions of the traveling-wave type have also been obtained.
Reviewer: L.Shih

MSC:
35Q99PDE of mathematical physics and other areas
35B40Asymptotic behavior of solutions of PDE
35G20General theory of nonlinear higher-order PDE