超对称扩展KdV方程的超黎曼theta函数周期波解及渐近性质

Super Riemann Theta Function Periodic Wave Solutions and Asymptotic Properties of the Supersymmetric Extended KdV Equation

【目的】研究超对称扩展KdV方程的超黎曼theta函数周期波解及渐近性质。【方法】基于直接法导出流体力学中扩展KdV方程对应的超对称方程。利用Hirota双线性方法推出超对称扩展KdV方程的双线性形式及超孤波解。利用广义的多维黎曼theta函数和超Hirota双线性形式,构造超对称扩展KdV方程的超黎曼theta函数周期波解。【结果】首先得到了流体力学中扩展KdV方程对应的超对称方程以及该超对称方程的双线性形式及超孤波解。其次推出了超对称扩展KdV方程的超黎曼theta函数周期波解,最后分析了周期波解的渐近性质。【结论】周期波解在Grassmann变量的影响下出现了一个有趣的影响带,而且关于这个影响带是对称的,且会随着这个影响带一起衰退。在某些“小振幅”极限下,超周期波解趋向于超孤波解。

[Purposes]The super Riemann theta function periodic wave solutions and asymptotic properties of the supersymmetric extended KdV equation are studied. [Methods]The supersymmetric equation corresponding to the extended KdV equation in fluid mechanics is derived based on the direct method. The bilinear form and super solitary wave solution of supersymmetric extended KdV equation are derived by using Hirota bilinear method. Using generalized multidimensional Riemann theta function and super Hirota bilinear form, the super Riemann theta function periodic wave solution of supersymmetric extended KdV equation is constructed. [Findings]Firstly, the supersymmetric equation corresponding to the extended KdV equation in fluid mechanics, and its bilinear form and super solitary wave solution are obtained. Secondly, the periodic wave solution of super Riemann theta function of supersymmetric extended KdV equation is derived. Finally, the asymptotic properties of the periodic wave solution are analyzed.[Conclusions]Under the influence of Grassmann variable, an interesting influence band appears in the periodic wave solution, and the influence band is symmetrical and decays with it. Under some “small amplitude” limits, the super periodic wave solution tends to the super solitary wave solution.