Multiple optical kink solutions for new Painleve integrable (3+1)-dimensional sine-Gordon equations with constant and time-dependent coefficients

This work establishes entirely new Painleve integrable (3 +1)-dimensional sine-Gordon equations. The first equation is characterized with constant coefficients that nicely passes the Painleve property to emphasize its integrability, the other model, with time-dependent coefficients, gives the compatibility conditions that exhibit the relations between the time-dependent coefficients. Multiple optical kink wave solutions will be reported for each equation.