Fourth-order recursion operators for third-order evolution equations

Marianna Euler
2008 Journal of Nonlinear Mathematical Physics  
We report the recursion operators for a class of symmetry integrable evolution equations of third order which admit fourth-order recursion operators. Under the given assumptions we obtain the complete list of equations, one of which is the well-known Krichever-Novikov equation. We consider the third-order evolution equation M Euler then (1) is said to be symmetry integrable [3] . Proposition: Equations of the form (1) which admit recursion operators of the form (2) under condition (3) are
more » ... ition (3) are exhausted by the following two cases:
doi:10.2991/jnmp.2008.15.2.2 fatcat:rq3rjkflojcwxg24n4j5lpjtlq