New peakon and multi-compacton solitary wave solutions of fully nonlinear sine-Gordon equation

In the paper, we introduce the concept of nonlinear intensity, study a fully nonlinear sine-Gordon equation SG(m, n, p) and obtain a new type of peakon solutions and kink solutions by a direct method. Research approximate SG(m, n, p) equation and obtain a new multi-compacton and peakon solutions of approximate SG(m, n, p) equation. At last, we study a fully nonlinear sine-Gordon equation under high dimension.