Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Abstract

The $(n+1)$-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the $m$th finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of $n=4$ various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

“…Nonlinear partial differential equations (NLPDEs) are extensively employed in the fields of science and engineering to represent and study a wide range of nonlinear phenomena encountered in practical applications [1][2][3][4][5][6][7][8][9][10][11][12][13]. These equations play a crucial role in modeling various scenarios, including fluid dynamics problems, wave propagation in complex media, seismic wave analysis, and the characterization of optical fibers.…”