Recursion Operators for a Class of Integrable Third‐Order Evolution Equations
Recursion Operators for a Class of Integrable Third‐Order Evolution Equations
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DOI：
10.1111/j.0022-2526.2004.01511.x
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发表时间：
2003-04
影响因子：
2.7
通讯作者：
N. Petersson;N. Euler;M. Euler
中科院分区：
文献类型：
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作者：
N. Petersson;N. Euler;M. Euler
对于 m、n、p、q、r、s 的函数形式，我们考虑 ut=uαuxxx+n(u)uuxux+m(u)u3x+r(u)uxx+p(u)u2x+q(u)ux+s(u)，其中 α= 0 和 α= 3，对于这些函数形式，方程在无限数量的李-巴克伦德对称意义上是可积的。为方程获得了与 x 和 t 无关的递归算子，它们生成这些无限组（局部）对称性。将势形式、光刻变换和 x 广义光刻变换的组合应用于所获得的方程。
We consider ut=uαuxxx+n(u)uxuxx+m(u)u3x+r(u)uxx+p(u)u2x+q(u)ux+s(u) with α= 0 and α= 3, for those functional forms of m, n, p, q, r, s for which the equation is integrable in the sense of an infinite number of Lie‐Bäcklund symmetries. Recursion operators which are x‐ and t‐independent that generate these infinite sets of (local) symmetries are obtained for the equations. A combination of potential forms, hodograph transformations, and x‐generalized hodograph transformations are applied to the obtained equations.