Existence of kink and anti-kink wave solutions for three physical models in mathematical physics

In this work, we consider three nonlinear physical models in mathematical physics through the tanh approach. This method is a strong tool to search for traveling waves resulting from one-dimensional nonlinear wave and nonlinear partial differential equations. This work contributes to a better understanding of kink and anti-kink soliton behavior in nonlinear systems, including dislocation dispersion in crystals, quantum field theory, shallow water, dust-acoustic waves, and nonlinear lattices. Two- and three-dimensional graphs are shown to illustrate the profile of the found solutions for appropriate free parameter values. In addition, we demonstrate how the physical characteristics affect how the solutions behave. Finally, the proposed technique may be applied to many equations emerging in mathematical physics.