The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer–Kaup–Kupershmidt equation

Abstract

By using the Chen et al. ansatz [Chen Y, Wang Q, Lang Y. Naturforsch 2005;60a:127] and by modifying our extended Fan sub-equation method [Yomba E. Phys Lett A 2005;336:463]. We have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerate Jacobi elliptic wave function-like solutions for the (2+1)-dimensional Broer–Kaup–Kupershmidt equation. The most important achievement of this method lies on the fact that we have succeeded in one move to give all the solutions which can previously be obtained by application of at least four methods (the method using the Riccati equation, or the first kind elliptic equation, or the auxiliary ordinary equation, or the generalized Riccati equation as mapping equation).