This section will focus on extracting the shock wave solutions to the KGZ equation (1) and (2) that are also known as topological soliton solution.

Finally, the numerical simulation that was conducted using finite difference scheme leads to the simulations for the topological soliton solutions.

In [5, 6], the ansatz method is applied to obtain the topological soliton solution of the generalized Rosenau-KdV equation.

Biswas, "Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity," Romanian Journal of Physics, vol.

Biswas, "Perturbation of

topological solitons due to sine-Gordon equation and its type," Communications in Nonlinear Science and Numerical Simulation, vol.

In this model, there appear particle-like excitations as topological solitons. Their mass is field energy only.

The investigations seem to support the conjecture that the particles we find in experiments are topological solitons characterised by topological quantum numbers.

of Kent, UK) provide discussion of the state of research concerning

topological solitons. Chapters contain discussion of solitons in classical field theories and the forces that exist between solitons, a survey of static and dynamic multi-soliton solutions, and discussion of kinks in one dimension, lumps and vortices in two dimensions, monopoles and Skyrmions in three dimensions, and instantons in four dimensions.