Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-11-09
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
We consider evolutionary equations of the form $u_t=F(u, w)$ where $w=D_x^{-1}D_yu$ is the nonlocality, and the right hand side $F$ is polynomial in the derivatives of $u$ and $w$. The recent paper \cite{FMN} provides a complete list of integrable third order equations of this kind. Here we extend the classification to fifth order equations. Besides the known examples of Kadomtsev-Petviashvili (KP), Veselov-Novikov (VN) and Harry Dym (HD) equations, as well as fifth order analogues and modifications thereof, our list contains a number of equations which are apparently new. We conjecture that our examples exhaust the list of scalar polynomial integrable equations with the nonlocality $w$. The classification procedure consists of two steps. First, we classify quasilinear systems which may (potentially) occur as dispersionless limits of integrable scalar evolutionary equations. After that we reconstruct dispersive terms based on the requirement of the inheritance of hydrodynamic reductions of the dispersionless limit by the full dispersive equation.
Ferapontov E. V.
Novikov Sergey V.
No associations
LandOfFree
On the classification of scalar evolutionary integrable equations in $2+1$ dimensions 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 classification of scalar evolutionary integrable equations in $2+1$ dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the classification of scalar evolutionary integrable equations in $2+1$ dimensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-494043