A Higher-Dimensionai Hirota Condition and Its Judging Method

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2008,（1）
• 页码范围: 27-30
• 页数: 4页
• 语种: 英文

摘要

When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F(Dt, Dx)f . F = O, Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As fax 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.