Lie symmetries of the nonlinear waves in the inhomogeneous Fisher-Kolmogorov equation

In this work we study a generalization of the Fisher-Kolmogorov equation from the point of view of the theory of symmetry reductions in partial differential equations. The reduction to partial differential equations in (1 + 1) dimension is derived from the optimal system of subalgebras. The invariance study of these equations leads to second-order ODEs. From these ODEs we derive exact solutions.In this work we study a generalization of the Fisher-Kolmogorov equation from the point of view of the theory of symmetry reductions in partial differential equations. The reduction to partial differential equations in (1 + 1) dimension is derived from the optimal system of subalgebras. The invariance study of these equations leads to second-order ODEs. From these ODEs we derive exact solutions.