Exact Solutions of (2+1)-Dimensional Euler Equation Found by Weak Darboux Transformation
LOU Sen-Yue1,2, LI Yi-Shen1,3
1Center of Nonlinear Science, Ningbo University, Ningbo 315211
2Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
3Department of Mathematics, and Center of Nonlinear Science, University of Science and Technology of China,Hefei 230026
Exact Solutions of (2+1)-Dimensional Euler Equation Found by Weak Darboux Transformation
LOU Sen-Yue1,2;LI Yi-Shen1,3
1Center of Nonlinear Science, Ningbo University, Ningbo 315211
2Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
3Department of Mathematics, and Center of Nonlinear Science, University of Science and Technology of China,Hefei 230026
Abstract： The weak Darboux transformation of the (2+1) dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as the Rossby waves can be simply obtained from the weak Darboux transformation with zero spectral parameters. The constant vorticity seed solution is utilized to generate Bessel waves.
2006, Vol. 23 
