Multi-soliton, rogue wave and periodic wave solutions of generalized \((2+1)\) dimensional Boussinesq equation (Q2657532)

The authors solve the Boussinesq equation \(u_{tt}-4u_{yt}+4u_{yy}-3u_{xy} +\frac{3}4 u_{xxxx} + \frac{3}2 u^2_{xx} = 0\) by the dependent variable transformation \(u(x, y, t) = 3(\log( f(x,y,t) ))_{xx}\) combined with Hirota's bilinear form. Single soliton, multi-soliton solutions including rogue, multi-travelling and singular periodic wave solutions are obtained and graphically displayed.