A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent ...

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated ...