Bifurcations of traveling wave solutions for the (2 + 1)-dimensional generalized asymmetric Nizhnik–Novikov–Veselov equation

By using the bifurcation theory of planar dynamical systems to the (2 + 1)-dimensional generalized asymmetric Nizhnik–Novikov–Veselov equation, the existence for solitary wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of these solutions mentioned are given. Furthermore, some exact explicit parametric expressions of these bounded traveling waves are obtained.