Contents 1 Introdu tion 12 Pde Properties 33 The Integrable NLS

Contents 1 Introdu tion 12 Problem Formulation 13 Graph properties of the matrix A

Perturbation theory for nearly integrable multi-component nonlinear PDEs

The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary perturbations and is given in the form of exact equations, which generate the sequence of approximate ODEs in successive orders with respect to the perturbation. ...

Integrable inhomogeneous NLS equations are equivalent to the standard NLS

A class of inhomogeneous nonlinear Schrödinger equations (NLS), claiming to be novel integrable systems with rich properties continues appearing in PhysRev and PRL. All such equations are shown to be not new but equivalent to the standard NLS, which trivially explains their integrability features. PACS no: 02.30.Ik , 04.20.Jb , 05.45.Yv , 02.30.Jr Time and again various forms of inhomogeneous n...

Non - Focusing Instabilities in Coupled ,

The nonlinear coupling of two scalar nonlinear Schrr odinger (NLS) elds results in non-focusing instabilities that exist independently of the well-known modulational instability of the focusing NLS equation. The focusing versus defocusing behavior of scalar NLS elds is a well-known model for the corresponding behavior of pulse transmission in optical bers in the anomalous (focusing) versus norm...

Exact Projective Excitations of Nonautonomous Nonlinear Schrödinger System in (1 + 1)-Dimensions

With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schrödinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, some periodic and localized excitations with novel properties are correspondingly revealed by entrancing appropriate system parameters. The integrable constraint conditions for the ...