Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions
Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions
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DOI：
10.1063/1.4817345
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发表时间：
2013-08
影响因子：
1.3
通讯作者：
M. Dimakos;A. Fokas
中科院分区：
文献类型：
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作者：
M. Dimakos;A. Fokas
在4+2中涉及两个标量函数的Davey-Stewartson型两方程组的可积推广，即，在四个空间和两个时间的维度，最近已经得出了作者之一。在这里，我们首先表明，存在一个减少这个系统的一个单一的方程，涉及一个标量函数在4+2;我们将这个方程称为4+2戴维-斯图尔特森方程。然后，我们表明，它是可能的，以减少这个方程在3+1，我们将称为3+1戴维-Stewartson方程。此外，通过采用所谓的直接线性化方法，我们计算了4+2和3+1 Davey-Stewartson方程的1-和2-孤子解。
An integrable generalisation of a Davey-Stewartson type system of two equations involving two scalar functions in 4+2, i.e., in four spatial and two temporal dimensions, has been recently derived by one of the authors. Here, we first show that there exists a reduction of this system to a single equation involving a scalar function in 4+2; we will refer to this equation as the 4+2 Davey-Stewartson equation. We then show that it is possible to reduce this equation to an equation in 3+1, which we will refer to as the 3+1 Davey-Stewartson equation. Furthermore, by employing the so-called direct linearising method, we compute 1- and 2-soliton solutions for both the 4+2 and the 3+1 Davey-Stewartson equations.