arXiv subjects

Sergey Dremov

Publications and source records attributed to Sergey Dremov.

3 recordsLinked to original sources

arXiv2026

Numerical Direct Scattering Transform for Dark Solitons

We introduce a numerical direct scattering transform scheme for dark solitons of the nonlinear Schrodinger equation, enabling the identification and complete characterization of nonlinear coherent structures in defocusing media with a continuous-wave (CW) background. Our scheme is based on numerically solving the auxiliary Zakharov-Shabat scattering problem with CW boundary conditions and on analytically derived expressions that relate the elements of the transfer matrix to the scattering data for dark solitons and continuous-spectrum waves. To test our approach, we consider two analytically solvable cases of the scattering problem: i) rectangular, and ii) hyperbolic tangent hollows in the CW background, which can contain an arbitrary number of dark solitons, with known scattering data. We revisit the analytical derivations and obtain a complete set of soliton parameters represented by discrete eigenvalues and norming constants. By supplementing the direct scattering transform algorithm with high-precision arithmetic to accurately recover soliton norming constants, we provide a robust method to analyze data from numerical or natural experiments on complex wave fields in optical, hydrodynamical, and other physical systems.

nlin.PS↗

arXiv2026

Eigenvalue-Based Approach to Manipulate and Reconstruct Nonlinear Pulses: Towards Soliton Tomography

Soliton content of nonlinear pulses of different physical nature is universally characterized by a discrete set of eigenvalues. In an ideal channel governed by the nonlinear Schrodinger equation, the eigenvalues do not change along the wave field propagation. Perturbations leave predictable fingerprints on the eigenvalue portrait, which was recently used to manipulate optical fiber solitons in [Phys. Rev. Lett. 134, 193804, 2025]. Here, we develop a theoretical framework to manipulate and reconstruct sech-shaped nonlinear wave fields based on soliton eigenvalue response functions and the corresponding inverse problem. We derive analytical expressions to enable nonlinear manipulation of solitons by applying instant, controllable perturbations. Then we present a concept of perturbation sensing with the key feature of nonlinear propagation of the probe signal over an unknown distance, enabling the extraction of information about the perturbation source hidden within nonlinear media or materials. We introduce an integral equation for the inverse problem of reconstructing the unknown shape of the wave field distortions, when the known observational data is a function of deviations in soliton eigenvalues measured at the end of the nonlinear propagation channel. We evaluate different reconstruction regimes and demonstrate a reliable inverse problem solution in presence of noise, paving the way towards soliton tomography.

nlin.PS↗

arXiv2023

Bi-solitons on the surface of a deep fluid: an inverse scattering transform perspective based on perturbation theory

We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures - bi-solitons - in the exact and approximate models for waves on the free surface of deep water. We generate numerically the bi-solitons of the approximate Dyachenko-Zakharov equation and fully nonlinear equations propagating without significant loss of energy for hundreds of the structure oscillation periods, which is hundreds of thousands of characteristic periods of the surface waves. To elucidate the long-living bi-soliton complex nature we apply an analytical-numerical approach based on the perturbation theory and the inverse scattering transform (IST) for the one-dimensional focusing nonlinear Schrödinger equation model. We observe a periodic energy and momentum exchange between solitons and continuous spectrum radiation resulting in repetitive oscillations of the coherent structure. We find that soliton eigenvalues oscillate on stable trajectories experiencing a slight drift on a scale of hundreds of the structure oscillation periods so that the eigenvalue dynamic is in good agreement with predictions of the IST perturbation theory. Based on the obtained results, we conclude that the IST perturbation theory justifies the existence of the long-living bi-solitons on the surface of deep water which emerge as a result of a balance between their dominant solitonic part and a portion of continuous spectrum radiation.

nlin.PS↗