Clay weekly context brief for the Nonlinear Sciences category (ISO week 2026-W41).

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. Persistence of kinks in the NLS equation with competing nonlinearities
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2610.02541
   External potentials break the translational invariance of nonlinear Schr\"odinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states.
2. Uncertainty quantification of holographic transport and energy loss for the hot and baryon-dense QGP
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2603.20482
   We investigate several transport coefficients across the phase diagram of a holographic Einstein-Maxwell-Dilaton (EMD) model of hot and dense QCD with $N_f=2+1$ flavors.
3. Measurement of the $^3$He Spin Structure Functions and Their Moments at Low Q$^2$
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2608.30101
   We report measurements of spin-dependent electron scattering from a polarized $^3$He target, $\vec{^3\textrm{He}}(\vec{e},e')X$, performed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab).
4. On the Cauchy Problem for the Sawada-Kotera Equation: Soliton resolution conjecture, Painlev\'e transcendents and asymptotic stability
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.03097
   We derive long-time asymptotics in different space-time regions for the Sawada-Kotera (SK) equation with admissible data involving continuous spectrum and finite discrete spectrum.
5. Attractor reconstruction in attracting subspaces: Slow-spectrum preshaping for reservoir computing under partial observation
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2606.24303
   Data-driven reproduction of chaotic dynamics under partial observation remains a challenge despite its practical importance.
6. Vector peakon equations and isospectral flows in Clifford algebras
   Source: nlin.PS (Pattern Formation and Solitons)
   Link: https://arxiv.org/abs/2606.17238
   Starting from a spectral problem posed in a Clifford algebra with $d$ generators and Euclidean signature, we study an integrable, coupled system of PDEs that can be viewed as a vector perturbation of the Camassa--Holm equation with residual orthogonal symmetry.
7. AI-Assisted GPU optimization of the Stochastic Variational Method for Few-Body Boson System
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.02745
   The stochastic variational method (SVM) is one of the most powerful methods to solve quantum few-body systems precisely in various fields, such as nuclear and atomic physics.
8. Laser Spectroscopy of Thulium Isotopes Near the (N=82) Shell Closure: Nuclear Moment and Charge Radius of ${}^{152\mathrm{m}}\mathrm{Tm}$
   Source: nucl-ex (Nuclear Experiment)
   Link: https://arxiv.org/abs/2607.25033
   We report on resonance ionization laser spectroscopy measurements performed on both neutron-deficient and neutron-rich thulium ($\mathrm{Tm}, Z=69$) isotopes.
9. Correlation functions of the 19-vertex IRF model and its integrable quantum spin-1 chain
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.03349
   We consider the interaction-round-a-face version of the nineteen-vertex model and derive a new quantum spin-$1$ chain.
10. Regularity and reentry basins of low Earth orbits in the $J_{2}$-solar radiation pressure problem
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2605.24575
   We numerically investigate the long-term dynamical structure of low Earth orbits (LEOs) using the Smaller Alignment Index (SALI), a fast numerical indicator of chaos, within a closed-form averaged model that incorporates the effects of solar radiation pressure and Earth's oblateness.
11. Total angular momentum distributions of fission fragments at scission in a 2-center basis
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.03270
   In this article, we propose a new method to calculate the angular momentum distribution of fis- sion fragments adapted to the case of 2-center axial basis used to solve the Hartree-Fock-Bogoliubov equations in view of fission studies.
12. A novel extension of the canonical 2+1-dimensional Dym equation. Moving boundary problems solvable via Painleve' II Reduction
   Source: nlin.SI (Exactly Solvable and Integrable Systems)
   Link: https://arxiv.org/abs/2610.02927
   An extension with temporal modulation is presented of the canonical 2 + 1-dimensional solitonic Dym equation as originally introduced by Konopelchenko and Dubrovsky.
13. Geodesic vortex detection on curved surfaces: Analyzing the 2002 austral stratospheric polar vortex warming event
   Source: nlin.CD (Chaotic Dynamics)
   Link: https://arxiv.org/abs/2501.03135
   Geodesic vortex detection is a tool in nonlinear dynamical systems to objectively identify transient vortices with flow-invariant boundaries that defy the typical deformation found in 2-d turbulence.
14. Energy-Resolved Spin and Parity Distributions of Fission Fragments
   Source: nucl-th (Nuclear Theory)
   Link: https://arxiv.org/abs/2610.03018
   Fission fragments are born rotating rapidly, but the evolution of this spin with excitation energy and its impact on fission observables remain largely unknown.

Sources in this brief: nlin.CD (Chaotic Dynamics); nlin.PS (Pattern Formation and Solitons); nlin.SI (Exactly Solvable and Integrable Systems); nucl-ex (Nuclear Experiment); nucl-th (Nuclear Theory).
Selected 14 of 17 available items for this weekly brief.