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

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.