Gerdjikov, Vladimir S and Grahovski, Georgi G (2024) On the N-waves hierarchy with constant boundary conditions. Spectral properties. International Journal of Geometric Methods in Modern Physics, 21 (10). DOI https://doi.org/10.1142/S0219887824400152
Gerdjikov, Vladimir S and Grahovski, Georgi G (2024) On the N-waves hierarchy with constant boundary conditions. Spectral properties. International Journal of Geometric Methods in Modern Physics, 21 (10). DOI https://doi.org/10.1142/S0219887824400152
Gerdjikov, Vladimir S and Grahovski, Georgi G (2024) On the N-waves hierarchy with constant boundary conditions. Spectral properties. International Journal of Geometric Methods in Modern Physics, 21 (10). DOI https://doi.org/10.1142/S0219887824400152
Abstract
The paper is devoted to $N$-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators $L$, whose potentials $Q(x,t)$ tend to constants $Q_\pm$ for $x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral properties of $L$, the direct scattering transform and construct its fundamental analytic solutions. We generalise Wronskian relations for the case of CBC -- this allows us to analyse the mapping between the scattering data and the $x$-derivative of the potential $Q_x$. Next, using the Wronskian relations we derive the dispersion laws for the $N$-wave hierarchy and describe the NLEE related to the given Lax operator.
Item Type: | Article |
---|---|
Additional Information: | 20 pages, 3 figures, LaTeX |
Uncontrolled Keywords: | N-wave interactions; Constant boundary conditions |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 25 Apr 2024 15:54 |
Last Modified: | 30 Oct 2024 21:24 |
URI: | http://repository.essex.ac.uk/id/eprint/38265 |
Available files
Filename: 2403.12925v1.pdf