A Generalization of the Hopf–Cole Transformation

A generalization of the Hopf–Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimensional diffusion equation with quadratic nonlinearity and of the Burgers equation are analyzed.