The Extended Fan Sub-Equation Method and its Application to the (2+1)-Dimensional Dispersive Long Wave and Whitham-Broer-Kaup Equations

Emmanuel Yomba

Chinese Journal of Physics

43卷4期（2005 / 08 / 01）

789 - 805

英文

An extended Fan sub-equation method is developed for searching for exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The most important achievement of this method lies in the fact that we have succeeded, in one move, to give all the solutions which have previously been obtained by the application of at least four methods. Consequently it is possible to connect the general elliptic equation involving five parameters to the other existing sub-equations involving three parameters like the Riccati equation, first kind of elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on. The solutions of the general elliptic equation are then mapped to those of the above mentioned sub-equations. As an illustration of the extended Fan method, some more new solutions are obtained for the (2+1)-dimensional dispersive long wave equation and the Whitham-Broer-Kaup (WBK) equation.