Optical solitons, nonlinear self-adjointness and conservation laws for Kundu-Eckhaus equation

In this article, Kundu-Eckhaus equation (KE) is studied from the perspective of modified tanh-coth method (MTC), extended Jacobi elliptic function expansion method (EJEF), Lie symmetry analysis, nonlinear self-adjointness and conservation laws (Cls). New soliton solutions like combined dark-bright, dark, periodic wave and singular soliton solutions are obtained. The equation is found to be a nonlinear self-adjoint, we construct the Cls using the new conservation theorem presented by Ibragimov. Physical interpretation for some of the obtained solutions are illustrated in Figures.