Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations
Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations
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DOI：
10.2991/jnmp.1998.5.2.10
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发表时间：
1998-04
影响因子：
0.7
通讯作者：
M. Velan;M. Lakshmanan
中科院分区：
文献类型：
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作者：
M. Velan;M. Lakshmanan
本文研究了最近引入的两个不同的(2+1)维非线性发展方程的Lie对称性、Kac-Moody-Virasoro代数、相似约化和特解。这两个方程是：(I)(2+1)维破裂孤子方程和(Ii)(2+1)维非线性Schrudinger型方程，它们是由Zakharov提出并后来由Strachan研究的。有趣的是，我们的研究表明，并不是所有的高维可积系统都有Kac-Moody-Virasoro型子代数。特别是，上面提到的两个可积系统不允许Virasoro型子代数，即使其他可积的高维系统允许这样的代数，我们也在附录中回顾了这一点。此外，对于这两个系统中对称性参数的特殊选择，我们还给出了物理上有趣的解。
Abstract In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schrudinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studies show that not all integrable higher dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly the two integrable systems mentioned above do not admit Virasoro type subalgebras, eventhough the other integrable higher dimensional systems do admit such algebras which we have also reviewed in the Appendix. Further, we bring out physically interesting solutions for special choices of the symmetry parameters in both the systems.