Lie analysis, conserved quantities and solitonic structures of Calogero-Degasperis-Fokas equation

Alexandria Engineering Journal

Farheen Ibraheem¹  Reza Abazari²  Adil Jhangeer³  Kenan Yildirim⁴  Hadi Rezazadeh⁵  Sumaira Sharif⁶ 

[1] Corresponding author.;Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran;Department of Mathematics, Namal Institute, 30KM Talagang Road, Mianwali 42250, Pakistan;Department of mathematics, Mus Alparslan University, Mus, Turkey;Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran;Faculty of Information Technology, University of Central Punjab, Lahore, Pakistan;

关键词: 70G65;    70H33;    35C07;    35C08;    35C09;   

DOI  :  

来源: DOAJ

【 摘 要 】

The paper investigates Calogero-Degasperis-Fokas (CDF) equation, an exactly solvable third order nonlinear evolution equation (Fokas, 1980). All possible functions for the unknown function F(ν) in the considered equation are listed that contains the nontrivial Lie point symmetries. Furthermore, nonlinear self-adjointness is considered and for the physical parameter A≠0 the equation is proved not strictly self-adjoint equation but it is quasi self-adjoint or more generally nonlinear self-adjoint equation. In addition, it is remarked that CDF equation admits a minimal set of Lie algebra under invariance test of Lie groups. Subsequently, Lie symmetry reductions of CDF equation are described with the assistance of an optimal system, which reduces the CDF equation into different ordinary differential equations. Besides, Lie symmetries are used to indicate the associated conservation laws. Also, the well-known (G′/G)-expansion approach is applied to obtain the exact solutions. These new periodic and solitary wave solutions are feasible to analyse many compound physical phenomena in the field of sciences.

【 授权许可】

Unknown