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nlin.SI2026
Integral Representations for Solutions of the Linearized Fourth Painleve Equation
Oleg M. Kiselev
We formulate the linearization of the fourth Painlevé equation as a linearized Hamiltonian system and transform the scalar variational equation to normal form, with the first-deriv…
math-ph2026
Small Denominators and Subresonant Accumulation in Weakly Nonlinear Dispersive Dynamics
P. Yu. Astafieva, O. M. Kiselev
We study a small-denominator mechanism in weakly nonlinear dispersive dynamics. After Fourier decomposition, a nonlinear dispersive equation becomes an infinite system of weakly co…
math.DS2026
A Minimal Bifurcation Model of Load Imbalance in a Softmax Mixture-of-Experts Router
O. M. Kiselev
We propose a minimal dynamical model of adaptive softmax routing for a two-expert Mixture-of-Experts (MoE) layer. The model is obtained as a mean-field limit of a discrete reinforc…