Quasiperiodic Wave Solutions of Supersymmetric KdV Equation in Superspace
Quasiperiodic Wave Solutions of Supersymmetric KdV Equation in Superspace
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DOI：
10.1111/j.1467-9590.2010.00491.x
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发表时间：
2010-11
影响因子：
2.7
通讯作者：
E. Fan;Y. Hon
中科院分区：
文献类型：
--
作者：
E. Fan;Y. Hon
提出了一种直接统一的超空间中显式构造超对称KdV方程准周期波解（多周期波解）的方案。该方案基于超 Hirota 形式的概念和超黎曼 theta 函数的使用。与普通的纯玻色子场的KdV方程相比，费米子场的超对称KdV方程出现了超准周期波的一些新现象。例如，结果表明，对于任意参数，超对称 KdV 方程不具有 N≥ 2 的 N 周期波解。进一步观察到，在格拉斯曼变量存在的情况下，准周期波之间出现了一个影响带。准周期波关于能带对称，但随能带塌缩。此外，严格建立了准周期波解和孤子解之间的关系。结果表明，在一定条件和小振幅限制下，准周期波解收敛于孤子解。
A direct and unifying scheme for explicitly constructing quasiperiodic wave solutions (multiperiodic wave solutions) of supersymmetric KdV equation in a superspace is proposed. The scheme is based on the concept of super Hirota forms and on the use of super Riemann theta functions. In contrast to ordinary KdV equation with purely bosonic field, some new phenomena on super quasiperiodic waves occur in the supersymmetric KdV equation with the fermionic field. For instance, it is shown that the supersymmetric KdV equation does not possess an N‐periodic wave solution for N≥ 2 for arbitrary parameters. It is further observed that there is an influencing band occurred among the quasiperiodic waves under the presence of the Grassmann variable. The quasiperiodic waves are symmetric about the band but collapse along with the band. In addition, the relations between the quasiperiodic wave solutions and soliton solutions are rigorously established. It is shown that quasiperiodic wave solution convergence to the soliton solutions under certain conditions and small amplitude limit.