Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-05-13
Nonlinear Sciences
Exactly Solvable and Integrable Systems
20 pages, 1 fugure
Scientific paper
We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of nonlinear PDEs linearizable by the matrix Hopf-Cole substitution (the B\"urgers hierarchy). We derive examples of four-dimensional nonlinear matrix PDEs together with they scalar and three-dimensional reductions. Variants of the Kadomtsev-Petviashvili type and Korteweg-de Vries type equations are represented among them. Our algorithm is based on the combination of two Frobenius type reductions and special differential reduction imposed on the matrix fields of integrable PDEs. It is shown that the derived four-dimensional nonlinear PDEs admit arbitrary functions of two variables in their solution spaces which clarifies the integrability degree of these PDEs.
No associations
LandOfFree
Differential reductions of the Kadomtsev-Petviashvili equation and associated higher dimensional nonlinear PDEs 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 Differential reductions of the Kadomtsev-Petviashvili equation and associated higher dimensional nonlinear PDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differential reductions of the Kadomtsev-Petviashvili equation and associated higher dimensional nonlinear PDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-129135