New Explicit Solutions of the Extended Double (2+1)-Dimensional Sine-Gorden Equation and Its Time Fractional Form

In this paper, the extended double (2+1)-dimensional sine-Gorden equation is studied. First of all, using symmetry method, corresponding vector fields, Lie algebra and infinitesimal generators are derived. Then, from generators, reductions presented. addition, these reduced equations converted into partial differential equations, which including classical (1+1)-dimensional equation. Moreover, based on method again, investigated. Meanwhile, traveling wave transformation, some explicit solutions obtained. Consequently, a conservation law derived via multiplier method. Finally, especially with help fractional complex transform, time also These results might explain nonlinear phenomenon.