New patterns of localized excitations in (2+1)-dimensions: The fifth-order asymmetric Nizhnik–Novikov–Veselov equation

By applying the mastersymmetry of degree one to the time-independent symmetry K1, the fifth-order asymmetric Nizhnik–Novikov–Veselov system is derived. The variable separation solution is obtained by using the truncated Painlevé expansion with a special seed solution. New patterns of localized excitations, such as dromioff, instanton moving on a curved line, and tempo-spatial breather, are constructed. Additionally, fission or fusion solitary wave solutions are presented, graphically illustrated by several interesting examples.