Application of Lie-Group Theory for solving CalogeroBogoyavlenskii- Schiff Equation

Abstract

This work deals with exact solutions of (2+1)-dimensional

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.…”

A Note on the Lie Algebra of the Invariants in the CBS Nonlinear Equation

“…The Calogero-Bogoyavleskii-Schiff Nonlinear Partial can be written as [1] The study of the integrability of this equation has been the subject of a large body of literature concerning specially the solutions obtained by means of a wealth of methods. For instance the interested reader may wish to check the references [2], [3], [4] and [5]. To achieve this goal the method of the Singular Manifold Expansion has been extensively used.…”

Exact solutions of Calgero–Bogoyavlenskii–Schiff equation using the singular manifold method after Lie reductions

“…In 2015, Gomez through the Tanh–Coth method derived analytical solutions of the CBS equation. In 2016, Kumar derived an exact solution for CBS via a similarity transformations method.…”

“…In 2015, Gomez [14] through the Tanh-Coth method derived analytical solutions of the CBS equation. In 2016, Kumar [15] derived an exact solution for CBS via a similarity transformations method. Here, CBS .2 C 1/-dimensional equation is transformed to an ODE through two successive Lie reductions [16,17].…”