Related papers: Spectral curves for the rogue waves
In this Thesis, we study the behavior of spectral curves of quantum graphs under certain families of vertex conditions, called the $\delta_s$ family, which we define in this work. We focus on studying two main quantities related to the…
Spatially-bounded rogue waves, i.e., rogue waves that arise in a limited region of a multi-dimensional space, are interesting and important from both theoretical and applied points of view. In this paper, we determine spatially-bounded…
Spectrograms provide an efficient way to analyse surface elevation signals of ship waves taken from a sensor fixed at a single point in space. Recent work based on a simplified model for the ship's disturbance suggests that matching the…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS…
Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topological entropy of the Smale space.
Rogue waves in birefringent optical fibers are analyzed within the framework of the coupled nonlinear Schr\"odinger (CNLS) system. The generation of rogue waves is frequently associated with modulation instability (MI). It is commonly…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
Vortices are screw phase dislocations associated with helicoidal wave-fronts. In nonlinear optics, vortices arise as singular solutions to the phase-intensity equations of geometric optics. They exist for a general class of nonlinear…
We construct a family of explicit rotational solutions to the nonlinear governing equations for water waves, describing edge waves propagating over a plane-sloping beach. A detailed analysis of the edge wave dynamics and of the run-up…
In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…
The phase or orbital light curves of extrasolar terrestrial planets in reflected or emitted light will contain information about their atmospheres and surfaces complementary to data obtained by other techniques such as spectrosopy. We show…
We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…
We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…
The explicit solution to the spectral problem of quantum graphs found recently in \cite{Anima}, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
There have been recent advances in the construction of algebraic curves for certain classes of string solutions in the context of the AdS/CFT correspondence. In this paper we obtain the Lax operators and associated spectral curves for…
Prediction is a central goal and a yet-unresolved challenge in the investigation of oceanic rogue waves. Here we define a horizon of predictability for oceanic rogue waves and derive, via extensive computational experiments, the first…
In this paper spectral methods are applied to investigate the hydrodynamic instability of swirling flow with application to Francis hydraulic turbine. Spectral methods imply representing the problem solution as truncated series of smooth…