A higher-dimensional Hirota condition and its judging method

作者：Guo Fu Kui^*; Mang Yu Feng

来源：Communications in Theoretical Physics, 2008, 49(1): 27-30.

• Hirota condition
• KdV equation
• soliton solution

When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F(D-t, D-x)f . f = 0, Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go, a similar condition is established in this paper, also we call it a higher-dimensional Hirota condition, a corresponding judging theory is given. As its applications, a few two-dimensional KdV-type equations possessing arbitrary N-soliton solutions are obtained.

• 出版日期2008-1-15
• 单位山东大学