Multilinear Variable Separation Approach in (3+1)-Dimensions:
the Burgers Equation
YING Jin-Ping1,2, LOU Sen-Yue1,3,4
1Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
2Zhejiang Business Technology Institute, Ningbo 315012
3School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
4Department of Physics, Ningbo University, Ningbo 315211
Multilinear Variable Separation Approach in (3+1)-Dimensions:
the Burgers Equation
YING Jin-Ping1,2;LOU Sen-Yue1,3,4
1Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
2Zhejiang Business Technology Institute, Ningbo 315012
3School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
4Department of Physics, Ningbo University, Ningbo 315211
Abstract： The multi-linear variable separation approach has been proven 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.
2003, Vol. 20 
