Recursion Operators of Some Equations of Hydrodynamic Type

Abstract

We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two higher symmetries and their recursion operators. We also discuss a reduction of $N+1$ systems to $N$ systems of some new equations of hydrodynamic type.

Latex File (amssymb), 22 pages

Cited by in corpus (5)

• Discrete Symmetries and Nonlocal Reductions
• Nonlocal Hydrodynamic Type of Equations
• Recursion Operator and Rational Lax Representation
• Recursion operators for KP, mKP and Harry-Dym Hierarchies
• Hydrodynamic type integrable equations on a segment and a half-line