Multi-wave, breather and interaction solutions to (3+1) dimensional sine-Gordon equation arising in nonlinear physical sciences

Based on the Hirota bilinear forms, the multi-wave solutions of the (3 + 1) dimensional sine-Gordon equation with various physical properties were constructed with using symbolic computation. This equation is characterized by constant coefficients that can be integrated in the Painleve sense. Double exponential and homoclinic breather approaches are used to obtain solutions. In addition, the interaction phenomenon between the exponential function, sine function and the hyperbolic sine function are constructed. For a better understanding the dynamics of the underlying equation three dimensional, density and contour graphs are demonstrated for the appropriately selected parameters. Thus, it has become more possible to observe the physical behaviors of the solutions. The results obtained in this study will contribute to the expansion and enrichment of the solution forms available in the literature of the model under consideration. The results obtained could have important applications in nonlinear optics, solid state physics, optical solitons and quantum field theory.