Journal of Nonlinear Mathematical Physics

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 third...

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 have...

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 coupled...