In this paper, the Painlevé integrable property of (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, Bäcklund transformations for gBK are derived by using truncation. Based on a special case transformations, linearized into heat conduction equation. Inspired reduced Burgers Starting from linear equation, two forms N-soliton solutions and rational with singularity...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to k−constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with sel...

In this present work we applied the direct algebraic method to Broer-Kaup-Kupershmidt system. Then new types of complex solutions are obtained to the Broer-Kaup-Kupershmidt system.