On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

Details On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

2009-01-06

arxiv.org/abs/0901.0647v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, 1 figure

Scientific paper

It was shown recently that Frobenius reduction of the matrix fields reveals interesting relations among the nonlinear Partial Differential Equations (PDEs) integrable by the Inverse Spectral Transform Method ($S$-integrable PDEs), linearizable by the Hoph-Cole substitution ($C$-integrable PDEs) and integrable by the method of characteristics ($Ch$-integrable PDEs). However, only two classes of $S$-integrable PDEs have been involved: soliton equations like Korteweg-de Vries, Nonlinear Shr\"odinger, Kadomtsev-Petviashvili and Davey-Stewartson equations, and $GL(N,\CC)$ Self-dual type PDEs, like Yang-Mills equation. In this paper we consider the simple five-dimensional nonlinear PDE from another class of $S$-integrable PDEs, namely, scalar nonlinear PDE which is commutativity condition of the pair of vector fields. We show its origin from the (1+1)-dimensional hierarchy of $Ch$-integrable PDEs after certain composition of Frobenius type and differential reductions imposed on the matrix fields. Matrix generalization of the above scalar nonlinear PDE will be derived as well.

Affiliated with

Also associated with

No associations

Rating

On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-632341