一类Jimbo-Miwa型方程的集中解
Lump Solutions to a Jimbo-Miwa Like Equations
摘要：
通过一个具有广义双线性导数的广义双线性方程，得到了（3+1）维Jimbo-Miwa型非线性微分方程.基于广义双线性形式，通过对Jimbo-Miwa型方程的二次多项式函数解的Maple搜索，得到了两类在空间各个方向上合理局部化的集中解和一类复集中型解.给出了保证解的解析性和合理局部化的适当条件。每个得到的集总解决方案持有六个自由参数，其中两个是由于Jimbo-Miwa类方程的平移不变性，其中四个只需要满足所提出的适当的条件是集总解决方案。我们还生成圆形或椭圆形的解决方案，从所获得的解决方案，使用不同的条件上的肿块解决方案。此外，还给出了直观的图形来说明显式解的性质.
英文摘要：
A Jimbo-Miwa like nonlinear differential equation in (3+1)-dimensions is developed through a generalized bilinear equation with the generalized bilinear derivatives. Based on the generalized bilinear forms, two classes of lump solutions, rationally localized in all directions in the space, and a class of complex lump type solution are generated from a Maple search of quadratic polynomial function solution to the proposed Jimbo-Miwa like equation. The apposite conditions to assurance analyticity and rational localization of the solutions are offered. Each of the resulting lump solutions hold six free parameters, two of which are due to the translation invariance of the Jimbo-Miwa like equations and four of which only require to satisfy the presented apposite conditions of being lump solutions. We also generate circle or ellipse shape solutions from the obtained solutions using different conditions on the lumps solutions. Moreover, figures are given to visualize the properties of the explicit solutions.
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