Journal of Nonlinear Mathematical Physics

Volume 9, Issue 2, May 2001

1. Mixed Perturbative Expansion: the Validity of a Model for the Cascading

Hervé LEBLOND
Pages: 126 - 143
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...

2. Invariant Sets and Explicit Solutions to a Third-Order Model for the Shearless Stratified Turbulent Flow

V N GREBENEV, B B ILYUSHIN
Pages: 144 - 156
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...

3. Functional Representation of the Ablowitz­Ladik Hierarchy. II

V E VEKSLERCHIK
Pages: 157 - 180
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...

4. Reflectionless Analytic Difference Operators III. Hilbert Space Aspects

S N M RUIJSENAARS
Pages: 181 - 209
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...

5. Time-Dependent Recursion Operators and Symmetries

M G ÜRSES, A KARASU, R TURHAN
Pages: 210 - 228
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...

6. On Complete Integrability of the Generalized Weierstrass System

P BRACKEN, A M GRUNDLAND
Pages: 229 - 247
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...