Nonlinear self adjointness and exact solution of Fokas-Olver-Rosenau-Qiao (FORQ) equation

Based on Lie’s symmetry approach, conservation laws are constructed for Fokas-Olver-Rosenau-Qiao(FORQ) equation and exact solution is obtained. Nonlocal conservation theorem is used to carry out the analysis of conservation process. Nonlinear self adjointness concept is applied to FORQ equation, it is proved to be strict self adjoint. Characteristic equation and similarity variable help us find exact solution of FORQ equation. Compared with solutions found in previous papers, our solution is new and important, since it is not possible to find exact solution of FORQ equation quite easily.