TY - JOUR

T1 - Inverse scattering transform: From solving equations to facilitating analysis of coherent structures

AU - Chekhovskoy, I. S.

AU - Shtyrina, O. V.

AU - Fedoruk, M. P.

AU - Turitsyn, S. K.

N1 - Chekhovskoy, I. S., Shtyrina, O. V., Fedoruk, M. P., & Turitsyn, S. K. (2026). Inverse scattering transform: From solving equations to facilitating analysis of coherent structures. Physica D: Nonlinear Phenomena, 497, 135366. https://doi.org/10.1016/j.physd.2026.135366 This work was supported by the RSF grant 25-61-00010, https: //rscf.ru/project/25-61-00010/ (M.P.F. and I.S.Ch.) and by the state funding program FSUS-2025-0010 (O.V.Sh.). Work of S.K.T. was supported by the Engineering and Physical Sciences Research Council grant EP/W002868/1.

PY - 2026/11

Y1 - 2026/11

N2 - We overview and expand recent results on the complementary use of the inverse scattering transform (IST) (also known as the nonlinear Fourier transform, NFT) as a characterization technique rather than a method for solving integrable equations. Here we systematize the IST/NFT-based analysis of non-integrable dissipative dynamics and adapt it to the description of laser light dynamics obeying the Haus-Ginzburg-Landau equation (HGLE), clarifying when the low-dimensional soliton-based description is accurate. This approach may help analyze localized coherent structures in physical systems beyond integrable models, including dissipative nonlinear systems ranging from photonics to the ocean waves. Using the IST, one can reduce the effective degrees of freedom in a nonlinear system when coherent structures dominate the dynamics. As an example of this application, without loss of generality, we consider a heuristic generalized Haus-Ginzburg-Landau model that illustrates the fundamental effects of optical pulse generation from noise in lasers.

AB - We overview and expand recent results on the complementary use of the inverse scattering transform (IST) (also known as the nonlinear Fourier transform, NFT) as a characterization technique rather than a method for solving integrable equations. Here we systematize the IST/NFT-based analysis of non-integrable dissipative dynamics and adapt it to the description of laser light dynamics obeying the Haus-Ginzburg-Landau equation (HGLE), clarifying when the low-dimensional soliton-based description is accurate. This approach may help analyze localized coherent structures in physical systems beyond integrable models, including dissipative nonlinear systems ranging from photonics to the ocean waves. Using the IST, one can reduce the effective degrees of freedom in a nonlinear system when coherent structures dominate the dynamics. As an example of this application, without loss of generality, we consider a heuristic generalized Haus-Ginzburg-Landau model that illustrates the fundamental effects of optical pulse generation from noise in lasers.

KW - Уравнение Хауса-Гинзбурга-Ландау

KW - Нелинейное преобразование Фурье

KW - Обратное преобразование рассеяния

KW - NLSE-солитоны

KW - Теория возмущений

KW - Haus-Ginzburg-Landau equation

KW - Inverse scattering transform

KW - NLSE Solitons

KW - Nonlinear fourier transform

KW - Perturbation theory

UR - https://www.mendeley.com/catalogue/95bc64c4-caf4-3c19-86c5-ce1ad4c191f1/

UR - https://www.scopus.com/pages/publications/105047673666

U2 - 10.1016/j.physd.2026.135366

DO - 10.1016/j.physd.2026.135366

M3 - Article

VL - 497

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -