Abstract
The bifurcation theory for planar dynamical systems is applied to the traveling wave system corresponding to the(2+1)-dimensional nonlinear Nizhnik-Novikov-Veselov dynamical equation. For certain values of the bifurcation parameters, we introduce new traveling wave solutions. These solutions are expressed in terms of elliptic Jacobi functions and Weierstrass elliptic function. These solutions are graphically clarified.