A novel class of solutions for the \((2+1)\)-dimensional higher-order Broer-Kaup system (Q524678)

This paper concerns the following \((2 + 1)\)-dimensional higher-order Broer-Kaup system: \[ \begin{cases} u_t + 4(u_{xx} + u^3 - 3uu_x + 3uw + 3p)_x = 0, \\ v_t + 4(v_{xx} + 3vu^2 + uv_x + 3vw)_x = 0, \\ w_y -v_x = 0, \\ p_y - (uv)_x = 0. \end{cases} \] A detailed symmetry analysis for the Broer-Kaup System is presented. Among others, a classification of symmetry reductions of the Broer-Kaup System by \(2\)-dimensional subalgebras (up to conjugacy) of symmetry algebra is given.