Multilinear Variable Separation Approach in (3+1)-Dimensions: the Burgers Equation

The multi-linear variable separation approach has been proved to be very useful in solving many (2+1)-dimensional integrable systems. Taking the (3+1)-dimensional Burgers equation as a simple example, here we extend the multi-linear variable separation approach to (3+1)-dimensions. The form of the universal formula obtained from many (2+1)-dimensional system is still valid. However, a more general arbitrary function (with three independent variables) has been included in the formula. Starting from the universal formula, one may obtain abundant (3+1)-dimensional localized excitations. In particular, we display a special paraboloid-type camber soliton solution and a dipole-type dromion solution which is localized in all directions.