Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W45). Clay tracks publications from the Nonlinear Sciences feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed. Recent publications: 1. Absorption of bound supernova axion-like particles by the neutron star weakens the heating limits on their photon coupling Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2610.39402 Axion-like particles (ALPs) that couple to protons are produced in a core-collapse supernova, and the slow ones remain bound to the new neutron star. 2. Higher-order Approximate Symmetries Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2608.31098 The Fushchych--Shtelen (FS) construction of approximate symmetries, based on a triangular system for the coefficients of a solution expansion, is extended to arbitrary order. 3. Wave Turbulence of Capillary Waves in Finite Systems Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2610.40217 We consider classical problem of turbulence of capillary waves. 4. Instability of exact finite-amplitude acoustic-gravity waves Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2610.35210 Godin (\textit{J. 5. Dynamical Coulomb effects on charged-pion HBT-radius splitting in central Au+Au collisions at few-GeV energies Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2609.23422 The pair transverse momentum ($k_T$) and collision-energy ($\sqrt{s_{NN}}$) dependent difference between $\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$ femtoscopic correlations was observed by the HADES and STAR Collaborations. 6. Stationary Action Principles for Neuronal Growth Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2610.36463 Neuronal growth is guided by biochemical, mechanical, and geometrical cues while being influenced by stochastic fluctuations in cytoskeletal dynamics, adhesion, and growth cone sensing. 7. Locally eventually onto cellular automata Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2610.33131 We give a new checkable criterion to ensure that a one-dimensional cellular automaton on a finite alphabet is locally eventually onto. 8. Muon-to-positron conversion from light Majorana neutrino exchange: nuclear responses and pion-pole-improved multipoles Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2610.39135 We study muon-to-positron conversion in nuclei that is mediated by light Majorana neutrinos, which probes lepton-number violation in the electron-muon sector. 9. Bootstrapping Fermionic $R$-operators with Decorated Yang--Baxter Equations Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2603.11172 Integrating infinitesimal generators of local dynamics into finite-time evolution is generally harder than extracting a local Hamiltonian from a quantum gate. 10. Topological defect trains excited by a boundary discontinuity in the two-dimensional complex Ginzburg-Landau equation Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2610.40103 With numerical simulations of the complex Ginzburg-Landau equation in a two-dimensional space, we find that a stationary but non-zero Dirichlet boundary condition with a discontinuity can drive a periodic train of evenly spaced topological defects that drift along and in proximity to the boundary. 11. Norm of resonance states in quantum scattering and electromagnetic systems Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2607.22052 Resonance states spatially diverge and are thus not square integrable. 12. Photoproduction of $J/\Psi$ in peripheral Oxygen-Oxygen collisions Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2605.12123 The photoproduction of $J/\Psi$ in peripheral Oxygen - Oxygen ($OO$) collisions at the Large Hadron Collider (LHC) is investigated considering distinct assumptions for the modeling of the nuclear photon flux, overlap function and dipole - proton scattering amplitude. 13. Condensation and optimal targeting of repeated forcing in heterogeneous networks Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2610.29714 Many networks receive repeated external forcing through a subset of entry nodes, for example infections imported from another population, information seeded by a campaign, or invasive species arriving through ports. 14. Idempotence criteria for lazy cellular automata Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2610.11811 A lazy cellular automaton $\tau:A^G\to A^G$ is determined by a finite neighborhood $S\subseteq G$ containing the group identity $e$, a pattern $p\in A^S$, and a writing symbol $a\in A\setminus\{p(e)\}$: its local rule is equal to the projection to $e$ except when it reads the pattern $p$, in which case it writes $a$. 15. Proton GTMDs and Wigner Distributions in the Chiral Quark Soliton Model: Orbital Angular Momentum and Spin-Orbit Correlation with Sea Quarks Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2610.39128 We calculate the leading-twist vector and axial-vector quark generalized transverse-momentum-dependent distributions (GTMDs) of the proton in the chiral quark soliton model, including both the discrete valence level and the regularized Dirac sea. 16. Invariant Reduction for Partial Differential Equations. III: Poisson Brackets Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2507.08213 We establish that local Hamiltonian operators admitted by systems of partial differential equations (PDEs) induce Poisson bivectors on suitable finite-dimensional subsystems describing invariant solutions. 17. Series approximation of discrete-soliton solutions of the DNLS equation Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2610.38461 We study standing waves of the discrete nonlinear Schr\"{o}dinger (DNLS) equation by means of perturbative series expansions in the inter-site coupling parameter $\varepsilon$. 18. Partial Reversibility and Counterdiabatic Driving in Nearly Integrable Systems Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2602.22317 Adiabatic (or reversible) processes are the key concept unifying our understanding of thermodynamics and dynamical systems. 19. Exploring differential two-particle correlations in $\gamma p$ and low-multiplicity pp collisions using PYTHIA8 Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2602.20345 A study of two-particle differential number ($B$) and transverse momentum ($P_{2}^\mathrm{CD}$) balance functions in photon-proton ($\gamma p$) and proton-proton (pp) collisions at $\sqrt{s}=$ 5.36 TeV is presented. 20. Ising-machine-like Driving Condition Restrictions in SSBM and Additional Pseudo-annealing- Driving Method for SSBM that Achieves Best Cut Value Search - Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2608.12545 In our previous work, we proposed and experimentally demonstrated a physics-based simulator for combinatorial optimization problems (SSBM), which exploits a distinctive spontaneous symmetry breaking (SSB) phenomenon identified in a dissipative system exhibiting robust causality described by an iterative equation. 21. Frobenius Revivals in Laplacian Cellular Automata: Replication, Entropy, and Information Recovery Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2511.17389 We investigate Frobenius revivals in prime-modulus Laplacian cellular automata. 22. Nonlinear response and retarded three-point correlators of charge transport Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2610.38571 We study nonlinear response of charge transport in relativistic kinetic theory within the relaxation time approximation. 23. MPS overlaps and Sklyanin determinants Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2610.37285 We derive explicit overlap functions for integrable matrix product states associated with arbitrary finite-dimensional irreducible evaluation representations of the orthogonal and symplectic twisted Yangians. 24. Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2610.36891 By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric $\phi^4$-like coupled equations in $x$ and $t$, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. 25. Physics-Inspired Optimizers beyond the Edge of Stability: Period-Two Orbits and Delayed Instability Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2610.27321 Gradient descent with momentum can be viewed as a particle moving with friction in the loss landscape. 26. Systematic calculations of \beta-delayed fission probabilities using a microscopic framework Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2610.37088 The process of $\beta$-delayed fission ($\beta$DF) consists of a mother nucleus $\beta$-decaying to different states of a daughter isotope, followed by fission of the latter with a probability that strongly depends on the energy of the states populated in the $\beta$ decay. 27. Predator-Prey Model: Driven Hunt for Accelerated Grokking Source: nlin.AO (Adaptation and Self-Organizing Systems) Link: https://arxiv.org/abs/2509.10562 A machine learning method is proposed using two agents (representing two coupled replicas of the model parameters) that simulate the biological behavior of a predator and a prey. 28. When do lazy and invertible cellular automata generate all cellular automata? Source: nlin.CG (Cellular Automata and Lattice Gases) Link: https://arxiv.org/abs/2610.18480 Let $G$ be a group and let $A$ be a set with at least two elements. 29. Gauge-parameter cancellation and finite form factors in one-loop quark scattering in the refined Gribov-Zwanziger framework Source: nucl-th (Nuclear Theory) Link: https://arxiv.org/abs/2610.38463 We calculate the one-loop amplitude for distinct-flavor massless quark scattering in a local BRST-invariant refined Gribov-Zwanziger theory with minimally coupled quarks. 30. The focusing coupled nonlinear Schr\"odinger equation with parallel nonzero boundary conditions: long--time asmptotics Source: nlin.SI (Exactly Solvable and Integrable Systems) Link: https://arxiv.org/abs/2610.37183 We study the long-time behavior of solutions of the focusing coupled nonlinear Schr\"odinger equations with parallel constant nonzero boundary conditions in the solitonless setting. 31. Bright Solitons in Non-Hermitian systems: Exploring the interplay of $\mathcal{PT}$ Symmetry and Wadati Structure Source: nlin.PS (Pattern Formation and Solitons) Link: https://arxiv.org/abs/2610.36706 In this study, we revisit the subject of optical solitons in non-Hermitian potentials. 32. Analog Realization and Measurement of a Forced Aliev-Panfilov Excitable Oscillator Source: nlin.CD (Chaotic Dynamics) Link: https://arxiv.org/abs/2610.40597 A single resistor moves a discrete analog realization of the forced Aliev-Panfilov excitable oscillator from a chaotic operating point of the model to a regular one. 33. Extracting the QCD speed of sound in the presence of quantum fluctuations Source: nucl-ex (Nuclear Experiment) Link: https://arxiv.org/abs/2610.36846 The equation of state of strongly interacting matter plays a %is one of the central quantities characterizing central role in characterizing quark--gluon plasma created in relativistic heavy-ion collisions. Sources in this brief: nlin.AO (Adaptation and Self-Organizing Systems); nlin.CD (Chaotic Dynamics); nlin.CG (Cellular Automata and Lattice Gases); nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems); nucl-ex (Nuclear Experiment); nucl-th (Nuclear Theory). Selected 33 of 466 available items for this weekly brief.