Some More Invariant Solutions of (2 + 1)-Water Waves

A revisit of symmetry analysis and group classifications of Boiti Leon Pempinelli system in (2+1)-dimensions

“…is Lie bracket defined by Table 1. The relation (8) helps to compile a table of the adjoint actions among each element in (6). All such adjoint actions are listed in the Table 2.…”

“…in the earlier works [3][4][5][6][7][8], a detailed groups classification of the infinite-dimensional Lie algebra ( 6) is obtained, and that too without assigning particular values to the arbitrary functions. One, two and three-dimensional groups classifications have been obtained at (11), ( 13), ( 14) respectively.…”

“…The equation (1) has been investigated for Lie symmetries in Refs. [3][4][5][6][7][8]. However, the symmetry analysis in all of these papers is incomplete and inadequate.…”

“…In Refs. [4,5], the arbitrary functions in an infinite Lie group are again fixed and group invariant solutions are obtained, and the authors used the same technique to fix arbitrary functions in their recent work [8]. Furthermore, in Ref.…”

Optimal Subalgebra of GKP by Using Killing Form, Conservation Law and Some More Solutions

“…Exact solutions of such systems can help in a better way to explain their complicated physical phenomena and the dynamical processes modeled by them. For instance, among the past researches [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], exact solutions of NPDEs play a vital role in the study of these complex physical phenomena. This literature review includes the previous findings [1][2][3][4][5][6][7][8][9][10][11][12] during the last decade.…”