Nonlinear wave excitations in the (2+1)-D asymmetric Nizhnik-Novikov-Veselov system

Abstract

The (2+1)-dimensional nonlinear asymmetric Nizhnik-Novikov-Veselov system is one of the extended versions of the Korteweg-de Vries equation, and as such of considerable significance in nonlinear wave dynamics. In this work, it is transformed into a bilinear form by using the Hirota transformation and then treated by the variable separation method. In particular, by separating variables in a specific manner, a class of solutions is obtained, which are constructed with the help of three auxiliary functions, Py, Ry, and Qxt. By selecting the three functions conveniently, we obtain novel nonlinear excitations for the asymmetric Nizhnik-Novikov-Veselov system. To make our results more explicit and interesting, various types of nonlinear profiles were displayed, colloquially named as the parallelogram, walnut, dark breather, half-moon breather, and the top-compressed quadrilateral breather structures. It is found that these local wave packets can be well controlled by appropriately selecting the three auxiliary functions, and that the variable separation approach can be extended to other high-dimensional nonlinear systems.