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1.
Bilinear Bcklund transformation and explicit solutions for a nonlinear evolution equation 下载免费PDF全文
The bilinear form of two nonlinear evolution equations are
derived by using Hirota derivative. The B\"{a}cklund transformation
based on the Hirota bilinear method for these two equations are
presented, respectively. As an application, the explicit solutions
including soliton and stationary rational solutions for these two
equations are obtained. 相似文献
2.
Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlev′e property of the(3+1)-dimensional Burgers equation, and then B¨acklund transformation is derived according to the truncated expansion of the obtained Painlev′e analysis. Using the B¨acklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures. 相似文献