(2 + 1) -dimensional Nonlinear Reaction Diffusion Equations Of The Invariant Set And The Exact Solution

Nonlinear PDEs actting as mathematical models is widely used in the fields of engineering and Natural Sciences. There are many key theoretical research and application research directions with regard to nonlinear PDEs, one of which is reduction to obtain exact solutions. At present, there is not a unified method to solve the nonlinear PDEs. Therefore, to find effective and innovative possible ways is still one of the important research fields of science research project.The idea of this paper is to discuss (2+1)-dimensional reaction-diffusion equation and its solutions in terms of the functional invariant sets E0={u:ux=vxF(u), uy=vyF(u)}, E1={u:ux=vxf(t)F(u),uy=vyf(t)F(u)}, E2={u:ux=a’(x)f(t)F(u), uy=b’(y)g(t)F(u)},where v is a smooth function of variables x and y, F(u) is a smooth function to be determined, a(x) is a smooth function of variable x, and b(y) is a smooth function of variable y. The solutions we get can provide practical significance for the research in other disciplines.