ALT In polar variables (x,θ) on a planar sector, we study a (1+2)D system (E2) derived from the three-dimensional axisymmetric Euler equations. Under a parity/symmetry ansatz on the whole meridian plane (odd/even reflection across the axes), we show that the velocity-pressure form of the 3D axisymmetric Euler system admits an exact reformulation in terms of Hou–Li type new variables (u,v,g). In the reformulated system (E2), the vortex stretching terms are greatly simplified (uv,v²-u²,-g²). This prompts us to treat (u,v,g) as the vorticity building blocks. Our first main result is an explicit construction of smooth solutions that blow up in finite time 0<T<∞ while a natural weighted energy remains uniformly bounded on [0,T], in particular staying finite at the blow-up time t=T. The construction proceeds in three steps. (1) We identify special ridge rays ±θ_0, 0<θ_0<π/2 such that, under the divergence-free constraint, system (E2) reduces on each ridge to a (1+1)D Constantin–Lax–Majda type co

ALT We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy R and the squared frequency ratio μ. By randomly sampling the isoenergetic volume to classify trajectories as oscillatory, rotational, or chaotic across the (μ, R) parameter plane, we obtain a global portrait of the coexistence and competition between dynamical regimes. The chaotic fraction is not uniformly distributed across the parameter plane but concentrates in a well-defined central cloud whose ridge follows a linear relation in the (μ, R) plane and whose maximum does not exceed 70% of the available phase space. The order-chaos-order transition is not a global property of the parameter plane but occurs specifically in the central region surrounding this cloud: along paths that traverse it, oscillatory orbits progressively give way to chaotic trajectories, which in turn yield to rotational orbits as the energy grows, revealing a clear se

ALT We introduce a continuous one-parameter family of elliptic sine-Gordon equations (SGE) characterized by the modulus 0 ≤ m ≤ 1 of Jacobi elliptic functions and analyze some of its properties and obtain its kink solution for various values of modulus m. These elliptic SGE have the novel property that while in the limit m = 0 they go over to the integrable sine-Gordon equation, in the m = 1 limit they go over to the integrable sine hyperbolic-Gordon equations (SHGE).

ALT In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of complete synchronization in the Sakaguchi-Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and induce complete synchronization in oscillators governed by phase-frustrated bi-harmonic coupling. We derive a general set of natural frequencies correlated with the network's degree heterogeneity, along with the parameters involved in the bi-harmonic coupling function that lead to complete synchronization (r=1) in the presence of the harmonic coupling terms (K₁, K₂ ≠ 0). On top of that, we found hysteresis in the synchronization transition in the case of scale-free networks, indicating a first-order (discontinuous) phase transition, whereas Erdos–Renyi networks exhibit a second-order (continuous) synchronization transition. Furthermore, we use mean-field approximation to determine the critical coupling strength for the synchronization transitio

ALT We present (m²/4)+ᵐ⁄₂+((1-(-1)ᵐ)/8) homogeneous (3m-2)-parameter families of Liouville integrable (2m)- and (2m-1)-dimensional Lotka-Volterra systems. We also study inhomogeneous versions of these systems.

ALT In the present work we revisit the problem of the dark solitary wave pinned in the discrete nonlinear Schrödinger equation. In a number of recent studies, the methodology of exponential asymptotics was attempted to be utilized in this problem, however the results were not found to be fully in agreement with associated multiprecision numerical computations. Here we resolve this conundrum by finding precise exponential asymptotics for the pinned dark solitary waves. Moreover, we reconcile the relevant result with a general theory of pinned dark solitary waves in the continuum nonlinear Schrödinger equations in the presence of external potentials.

ALT The multiplex network paradigm has been instrumental in revealing many unexpected phenomena and dynamical regimes in complex interacting systems. Nevertheless, most of the current research focuses on undirected multiplex structures, whereas real-world systems predominantly involve directed interactions. Here, we present an analytical framework for attaining optimal synchronization in directed multiplex networks composed of phase oscillators, considering both frustrated and non-frustrated regimes. A multiplex synchrony alignment function (MSAF) is introduced for this purpose, whose formulation integrates structural properties and dynamical characteristics of the individual directed layers. Using this function, we derive two classes of frequency distributions: one that yields perfect synchronization at a prescribed coupling strength in the presence of phase-lag, and another that optimizes synchronization over a broad range of coupling strengths. Numerical simulations on various directed

ALT Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from observed dynamics. This paper shows that the look-up table contains a readable causal architecture and introduces a forward model to extract it. The key observation in elementary cellular automata (ECA) is that adjacent cells share input positions, so the prime implicants of neighbouring transitions overlap. That overlap can couple the transitions causally or leave them independent. We formalize each pairwise interaction as a tile. A finite-state, tiling transducer, 𝒯, composes tiles across the CA lattice, tracking how coupling and independence propagate from one cell pair to the next. Structural properties of 𝒯 are used to classify ECA rules that can sustain regions of causal independence across space and time. We find that, in the 88 ECA equivalenc

ALT Synchronization is a ubiquitous phenomenon in nonequilibrium systems. One intriguing example found in every-day life is lifts installed next to each other, that move closely and arrive almost simultaneously during a busy time. However, the basic mechanism behind this lift synchronization is yet to be elucidated. Here, we investigate the effective interaction acting between the lifts quantitatively. Through the analysis on the time-series data obtained by numerically solving a rule-based discrete model of lifts, in which passengers at each floor show up stochastically and call a lift that is expected to arrive first, we find that the effective interaction acting between the lifts consists of not only attraction but also repulsion. By changing the parameters of the rule-based model, we are successful to tune the ratio of these competing interactions and to control the dynamics of lifts, realising the transition between in-phase and anti-phase synchronizations. Our strategy is applicable

ALT We present a comprehensive study of optical solitons supported by spiral potentials in media with the cubic-quintic (CQ) nonlinearity. A variety of families of stationary states, including fundamental and high-order (excited) in-phase, out-of-phase, and hybrid-phase ones, are found. The linear stability analysis, corroborated by direct simulations, demonstrates that all upper-branch nonlinear states in potentials with different azimuthal indices are completely stable, which rarely occurs in soliton physics. Our findings suggest spiral potentials as an effective means for multistable optical trapping, with potential applications in all-optical data processing.

ALT In this paper, the theory of inverse scattering transform (IST) is developed for the discrete PT-symmetric nonlocal nonlinear Schröinger equation under large nonzero boundary conditions (NZBCs). By considering that the data at infinity have constant amplitudes, two cases are studied where the previous IST theory fails for large NZBCs. Based on a suitable uniformization variable, the rigorous proofs for the analyticity, symmetries and asymptotic behaviors of the eigenfunctions and scattering coefficients are provided for the direc problem, and the potential reconstruction formula is derived by solving the Riemann-Hilbert problem. Particularly, the focusing equation is found to admit two types of novel solitons under large NZBCs: oscillating soliton and breather, where the former has not been previously reported, while the latter does not occur under small NZBCs. In addition, the multi-soliton solutions are shown to exhibit the collisions among oscillating dark/anti-dark solitons, and th

ALT The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are discussed. The less viscous, lower-density fluid fills the central region of the cylinder. Injecting a light fluid from below generates nonlinear cnoidal waves at the interface between the fluids, which have the appearance of soliton lattices. Two types of lattice dislocations are observed, the interaction between which is elastic. This experimental study fully confirms the theory of cnoidal waves and their dislocations for the KDV equation, which was developed 50 years ago and published in JETP [2].

ALT New determinant equalities were obtained based on the Wronskian formulas for a particular solution of the Volterra chain. Using the relationship between the Toda and Volterra chains, new first integrals for the Volterra chain are calculated using the first integrals for the Toda chain. Using the first integrals, a periodic Volterra chain with a period of five was considered.

ALT We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the neighborhood states, the central site takes either the majority state or the opposite and (ii) if the neighborhood states are tied, the central site either changes its current state or keeps it. The PCA is defined by two Bernoulli random variables with parameters p,r ∈ [0,1], and we analytically solve small size cases by using a Markov process formulation. We derive analytical expressions for the probability of asymptotically reaching each possible global configuration as a function of p and r, for all initial states. We show that for 0 < p,r < 1, the asymptotic probability distributions of achieving any of the states for the PCA are independent of the initial conditions. This contrasts with the behavior of the deterministic Wolfram's rules 23 (p=0,r=0)

ALT We consider a family of nonlinear oscillators, which is the autonomous case of the two-dimensional projective connection. We construct several classes of these oscillators that are simultaneously integrable and metrisable. This leads to families of (super)integrable two-dimensional metrics that are parametrized by arbitrary functions. In the superintegrable case we obtain an explicit expression for the unparametrized geodesics. In the integrable case we present two families of metrics with transcendental first integrals. We introduce the concept of generalized Darboux integrability in the context of both projective equations and geodesic flows. We demonstrate that the constructed integrable metrics are generalized Darboux integrable. In addition, we establish a direct connection between relative Killing vectors and invariants of the projective vector fields that are linear in the first derivative. Finally, we compute the dimensions of the projective Lie algebra for the obtained metrics

ALT Finite-size effects in the Kuramoto model are known to induce collective fluctuations even below the critical coupling, where the thermodynamic limit predicts complete asynchrony. While the shot-noise approach developed in our recent work accurately describes the power spectrum of these fluctuations for random frequency sampling, the present study reveals that the microscopic realization of the frequency distribution plays a crucial role. We show that a deterministic (quasi-uniform) selection of natural frequencies from the same Lorentzian distribution leads to qualitatively different dynamics: the shot noise spectrum exhibits anomalously slow oscillatory behavior, manifesting as wave-like patterns in time-frequency representations. The period of these oscillations scales linearly with the system size and matches the frequency spacing between neighboring oscillators near the distribution center. Numerical simulations confirm that these slow spectral dynamics arise from resonant interac

ALT An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of 𝒪(x⁻¹). The corresponding potential is related to a simple embedded eigenvalue in the Kaup–Newell spectral problem. This work focuses on the hierarchy of rational solutions of the MTM, in which the N-th member of the hierarchy describes a nonlinear superposition of N algebraic solitons with identical masses and corresponds to an embedded eigenvalue of algebraic multiplicity N. We show that the hierarchy of rational solutions can be constructed by using the double-Wronskian determinants. The novelty of this work is a rigorous proof that each solution is defined by a polynomial of degree N² with 2N arbitrary parameters, which admits N (N-1)/2 poles in the upper half-plane and N(N+1)/2 poles in the lower half-plane. Assuming that the leading-order polynomials have exactly N real roots, we show that the N-th member of the hierarchy describes the slow

ALT In this paper, we present a unified theoretical study of fluctuation-dominated transport and transverse thermoelectric response in two-dimensional superconducting films subjected to out-of-plane magnetic fields and electric-field drive. Our approach is based on the time-dependent Ginzburg-Landau equation with Langevin thermal noise, in which interaction effects of fluctuating Cooper pairs are incorporated self-consistently at the Gaussian (Hartree) level. We derive closed-form expressions for the fluctuation-induced Cooper-pair density, the renormalized resistance R(T,B⊥), and the nonlinear current response J(E,B⊥), explicitly accounting for the feedback of the electric field on the fluctuation spectrum. A central result is the emergence of an intrinsic S-shaped nonlinear J-E (or I-V) characteristic, featuring a negative-differential segment and multivalued solutions under voltage control. Within this framework, we introduce a physically transparent procedure to identify characteristic

ALT The transient time correlation function (TTCF) method is widely used in molecular fluids to compute non-equilibrium transport quantities, providing improved signal-to-noise ratios in ensemble averages without requiring prohibitively large sample sizes. In spite of its success in molecular and turbulent fluid systems, the method has not been systematically explored for more general non-equilibrium dynamical systems, including geophysical applications where the invariant measure is typically unknown. In this work, we present an analytical and numerical investigation of the TTCF method for computing nonlinear response functions in systems far from equilibrium. We discuss its relation to the spectral theory of stochastic systems, highlighting regimes where linear theory is insufficient and the advantages of TTCF. The aim of this work is to provide a framework for studying transient and steady-state responses using the TTCF approach in a broad class of nonequilibrium systems.