%0 Journal Article
%T A Generalization of the Hopf-Cole Transformation
%A Paulius Mi£¿kinis
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%X 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.
%K nonlocality
%K nonlinearity
%K diffusion equation
%K Burgers equation
%U http://dx.doi.org/10.3842/SIGMA.2013.016