New optical solitons of double Sine-Gordon equation using exact solutions methods

In this study, disparate analytical methodologies like the tan method, rational Exp-function method, sech method, extended tan method, and sine–cosine method are implemented to solve the double Sine-Gordon equation (DSG). Subsequently, the dynamical attributes of the obtained results have been underlined and depicted in terms of 3D and 2D graphical illustrations, likewise, different soliton solutions such as kink, bright-dark, and bright are depicted under an appropriate selection of parameters, and the existing criteria of these solitons are also given. A Survey of the literature shows that these methodologies are potent enough to extract exact solutions of differential equations applied in engineering mathematics.