In the first part of this paper we prove that flow associated to Burgers equation with a nonlocal term form fails be uniformly continuous from bounded sets for , and is Hilbert transform. Furthermore show cannot . We generalize result large class nonlinear transport-dispersive equations in any dimension, which particular contains Whitham paralinearization water waves system without surface tens...

We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These are obtained by a spin-pole ansatz including dynamical background term; we show that this solves sncILW provided spins and poles satisfy $A$-type Calogero-Moser (sCM) system certain constraints on initial The key to result is B\"{a}cklund transfo...

This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...