LAUSR

Abstract Here, we analyze the new optical solitons of the Ginsburg–Landau fractional complex of non-linearity (CGLE) laws in Kerr, which demonstrate various phenomena in physics such as non-linear waves, the transformation of the secondary phase, superconductivity, surfaces, liquid crystals, and field-theory strings. The new periodic solutions are obtained by the use of the extended Jacobian elliptic function (JEF) expansion method for the CGLE equation arising in physics. These solutions are practiced for three suggested definitions of derivative viz. conformable derivative, beta derivative, and M-truncated. Graphic depictions of the solutions obtained are also displayed. Some recent solitary waves have been found to be periodic, solitons-shock, conical, soliton-shock-like, super-soliton, localized soliton waves and other solutions can be directly evaluated.