Author: A. Sergyeyev
We generalize earlier results of Fokas and Liu and find all
locally analytic (1+1)-dimensional evolution equations of order n that admit
an N-shock type solution with N< n+2.
To this end, we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653-7660),
we completely characterized all (1+1)-dimensional evolution systems
that are conditionally invariant under a given generalized
(Lie-Baecklund) vector field
under the assumption that
the system of ODEs Q=0 is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a system of ODEs in t,
thus being a nonlinear counterpart to quasi-exactly solvable models in
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