A new type of perturbative expansion is built in order to give a rigorous derivation
and to clarify the range of validity of some commonly used model equations. This
model describes the evolution of the modulation of two short and localized pulses,
fundamental and second harmonic, propagating together...
We study dynamics of the shearless stratified turbulent flows. Using the method
of differential constraints we find a class of explicit solutions to the problem under
consideration and establish that the differential constraint obtained coincides with
the well-known ZemanLumley model for stratified...
In this paper we continue studies of the functional representation of the Ablowitz
Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition
we rederive the functional equations for the tau-functions of the ALH and obtain
some new equations which provide more straightforward...
In the previous two parts of this series of papers, we introduced and studied a large
class of analytic difference operators admitting reflectionless eigenfunctions, focusing
on algebraic and function-theoretic features in the first part, and on connections with
solitons in the second one. In this...
The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional itegrable evolution equations are considered. It has been previously observed that the
symmetries of the integrable evolution equations obtained through their recursion oerators do not satisfy the symmetry equations. There...
In this paper we study certain aspects of the complete integrability of the Generlized Weierstrass system in the context of the Sinh-Gordon type equation. Using the
conditional symmetry approach, we construct the Bäcklund transformation for the
Generalized Weierstrass system which is determined by...