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Residual Symmetry Reductions and Painlev\'e Solitons
Yan Li, Ya-Rong Xia, Ruo-Xia Yao, S. Y. Lou
https://arxiv.org/abs/2511.09077 https://arxiv.org/pdf/2511.09077 https://arxiv.org/html/2511.09077
arXiv:2511.09077v1 Announce Type: new
Abstract: This letter introduces the novel concept of Painlev\'e solitons -- waves arising from the interaction between Painlev\'e waves and solitons in integrable systems. Painlev\'e solitons may also be viewed as solitons propagating against a Painlev\'e wave background, in analogy with the established notion of elliptic solitons, which refer to solitons on an elliptic wave background. By employing a novel symmetry decomposition method aided by nonlocal residual symmetries, we explicitly construct (extended) Painlev\'e II solitons for the Korteweg-de Vries (KdV) equation and (extended) Painlev\'e IV solitons for the Boussinesq equation.
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On the integrable six-wave interaction system and its space-time shifted reduction
Mark J. Ablowitz, Ramesh Gupta, Ziad H. Musslimani, Nicholas J. Ossi
https://arxiv.org/abs/2510.10312

On the integrable six-wave interaction system and its space-time shifted reduction
The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell's equations, a reduced system of equations governing the dynamics of the electric and polarization fields are obtained. Using a space-time multi-scale asymptotic expansion, a hierarchy of coupled equations describing the spatio-temporal evolution of the perturbed electric and polarization fields are derived. The leading order equation admits a six-wave ansatz satisfying a triad…

Analysis of persistent and antipersistent time series with the Visibility Graph method
Macarena C\'adiz, Iv\'an Gallo-M\'endez, Pablo S. Moya, Denisse Past\'en
https://arxiv.org/abs/2510.01202

Analysis of persistent and antipersistent time series with the Visibility Graph method
In this work, we investigate a range of time series, including Gaussian noises (white, pink, and blue), stochastic processes (Ornstein-Uhlenbeck, fractional Brownian motion, and Levy flights), and chaotic systems (the logistic map), using the Visibility Graph (VG) method. We focus on the minimum number of data points required to use VG and on two key descriptors: the degree distribution P(k), which often follows a power law P(k) ~ k^-gamma, and the Hurst exponent H, which identifies persistent …