Study on New Doubly-periodic Solutions of two Coupled Nonlinear Wave Equations in Complex and Real Fields

0932–0784 / 04 / 0100–0029 $ 06.00 c © 2004 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com Knyzazev and Goncharenko [8] used two transformations to obtain one-kink and two-kink solutions. Recently we developed a powerful Weierstrass elliptic function expansion method and its general form in terms of Weierstrass elliptic functions [11, 12], which was applied to seek new doubly periodic solutions of some nonlinear wave equations [14]. This transformation is more general than the one due to Porubov [1], To the best of our knowledge, the doubly periodic solutions of the two systems (1) and (2) were not studied before. In this paper we extend the method to derive its doubly periodic solutions. Firstly we simply introduce the algorithm as follows: For a given nonlinear evolution equation, F(u,ut ,ux,uxt , ...) = 0, we seek its travelling wave solutions u(x, t) = u(ξ ),ξ = k(x− ct) in the form