The Broer-Kaup equation is one of many equations describing some phenomena shallow water wave. There are errors in scientific research because the existence non-smooth boundaries. In this paper, we generalize to fractal space and establish variational formulations through semi-inverse method. acquired formulation reveals conservation laws an energy form suggests possible solution structures mor...

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each the preceding equations, a Galilean type transformation between these $u_2$ previously known $u_2^{\prime}$ generated zero seed is given. We present several explicit formulas single-soliton for $u_2...

Generalized Cauchy matrix approach is used to investigate a discrete negative Ablowitz–Kaup–Newell–Segur (AKNS) equation. Several kinds of solutions more than multi-soliton this equation are derived by solving determining set. Furthermore, applying an appropriate continuum limit we obtain semidiscrete AKNS and after second derive the nonlinear The reductions discrete, semi-discrete continuous s...