Exotic localized structures based on the symmetrical lucas function of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov system

Abstract

Based on the Lucas Riccati method and a linear variable separation method, new variable separation solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov system are derived. Then, we give a positive answer for the following question: Are there any localized excitations derived by the use of another functions? For this purpose, some attention will be paid to dromion, peakon, multi dromion-solitoff excitations, regular fractal dromions, stochastic fractal dromion structure and combined structures including bell-like compactons, peakon-like compactons and compacton-like semi-foldons based on the golden main. With the help of the modified Weierstrass function, we discuss the stochastic fractal dromion structure both analytically and graphically. Finally, we conclude the paper and give some features and comments.