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Igor Chekhovskoy

Publications and source records attributed to Igor Chekhovskoy.

7 recordsLinked to original sources
arXiv2026

Fast eight-order Pade schemes based on Chebyshev polynomials for direct Zakharov-Shabat problem

In this work, we construct fast eighth-order Pade schemes for the direct Zakharov-Shabat scattering problem. The schemes are based on an eighth-order exponential integrator obtained from the Magnus expansion. A direct extension of the conventional fast Pade representation to the eighth-order case leads to insufficiently accurate fast variants in the considered tests. To overcome this difficulty, we reformulate the spectral dependence on a finite real interval using the Joukowski mapping and represent the local numerators and denominators in the Chebyshev polynomial basis. This makes it possible to construct the global transition matrix by a fast product tree while retaining a compact polynomial representation. Numerical experiments for chirped hyperbolic secant potentials with both signs of dispersion show that the proposed Chebyshev-based fast schemes substantially improve the accuracy of the corresponding direct fast variants and can be used for efficient computation of the continuous nonlinear spectrum.

math.NA↗
arXiv2026

Reservoir computing based on multicore fibers

Photonic reservoir computing offers a hardware-efficient route to processing temporal and sequential data, but delay-based implementations often rely heavily on temporal multiplexing, where long temporal masks are required to generate a sufficiently rich reservoir state. Here we show numerically that the spatial degrees of freedom of an active multicore fiber placed inside a delayed optical feedback loop can reduce this dependence on serial temporal encoding. The input signal is encoded by temporal and spatial masks, the pump distribution across the cores controls the reservoir operating point through the core-dependent effective gain and saturation energy, and the detected core intensities serve as readout features for a single trained linear layer. The system is modeled by linearly coupled nonlinear Schrödinger equations with saturable gain and solved using a split-step Fourier method. On the Mackey-Glass one-step-ahead prediction benchmark, a seven-core reservoir with equal temporal masks reduces the validation normalized root mean square error from 0.5956 for the single-core baseline to 0.0651 at a modulation rate of 40 GHz. At 1 GHz, spatial-only encoding reaches an error of 0.0323 using one temporal sample per symbol and no temporal mask. These results show that an active multicore fiber can provide both parallel readout channels and a tunable nonlinear transformation, offering a route to photonic reservoirs with reduced reliance on temporal multiplexing.

physics.optics↗
arXiv2020

Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications

Based on the generalized Cayley transform, a family of conservative one-step schemes of the sixth order of accuracy for the Zakharov-Shabat system is constructed. The exponential integrator is a special case. Schemes based on rational approximation allow the use of fast algorithms to solve the initial problem for a large number of values of the spectral parameter.

math.NA↗
arXiv2020

Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem

We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function $a(ζ)$, the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.

math.NA↗
arXiv2019

Fast Computation of the Direct Scattering Transform by Fourth Order Conservative Multi-Exponential Scheme

A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat system. The scheme represents a product of 13 exponential operators. The construction of the scheme is based on a fourth-order three-exponential scheme, which contains only one exponent with a spectral parameter. This exponent is factorized to the fourth-order with the Suzuki formula of 11 exponents. The obtained scheme allows the use of a fast algorithm in calculating the initial problem for a large number of spectral parameters and conserves the quadratic invariant exactly for real spectral parameters.

math.NA↗
arXiv2019

Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem

We propose two finite-difference algorithms of fourth order of accuracy for solving the initial problem of the Zakharov-Shabat system. Both schemes have the exponential form and conserve quadratic invariant of Zakharov-Shabat system. The second scheme contains the spectral parameter in exponent only and allows to apply the fast computational algorithm.

math.NA↗