Nonlinear Sciences Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences New submissions Cross-lists Replacements See recent articles Showing new listings for Monday, 17 August 2026 Total of 17 entries Showing up to 2000 entries per page: fewer | more | all New submissions (showing 6 of 6 entries) [1] arXiv:2608.13828 [pdf, html, other] Title: A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization J. de la Cruz, H.C. Rosu, G. Gonzalez, O. Cornejo-Perez Comments: 9 pages, 3 figures, 22 references Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Dynamical Systems (math.DS) We introduce a class of nonautonomous nonlinear oscillator equations of mixed Liénard type that arises from a parametric deformation of the commutative factorization procedure applied to second-order ordinary differential equations with periodic solutions. Their solutions, in particular the isochronous waveforms, are obtained in closed form through a Riccati reduction scheme for the power-law choice of the factorization function, $\phi(x)=kx^{q}$, $k\in \mathbb{R}$, and $q\in\mathbb{N}$, corresponding to the so-called modified Emden oscillators, and do not depend on the arbitrary deformation parameter $A_1$. The variational structure of the equation is characterised by a Lagrangian supplemented with a generalised Rayleigh dissipation function that contains a non-standard cubic term in $\dot{x}$. We also show that multiplying the equation of motion by the Jacobi multiplier $M(x)=x^{-2A_1}$ a position-dependent-mass (PDM) form is obtained with related friction and restoring force. [2] arXiv:2608.13950 [pdf, html, other] Title: Resilience Beyond Pairwise Networks Amitosh Tiwari, Chittaranjan Hens, Prosenjit Kundu Comments: 33 pages, 14 figures Subjects: Chaotic Dynamics (nlin.CD); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph) We derive a one-dimensional reduction for nonlinear dynamics on simplicial complexes containing both pairwise and triangular (higher-order) interactions. The effective state is defined using a mixed weight determined by the pairwise and triangular degrees of each node. The resulting reduced equation retains two structural coefficients, associated separately with the pairwise and higher-order coupling channels. A fluctuation expansion identifies the closure assumptions underlying the reduction and shows how deviations of individual node states from the effective state contribute to the approximation error. We numerically validate the proposed framework on Gene-regulatory dynamics, the double-well system, and SIS spreading. The states of the reduced model are compared with full-network simulations through coupling-parameter sweeps, steady-state branch calculations, and progressive node-removal experiments on synthetic and real-world networks. The reduced model successfully reproduces the principal transitions and steady-state branches in all three dynamical systems considered. Agreement is strongest for relatively homogeneous networks and deteriorates when structural heterogeneity produces a broader distribution of node states. The closure diagnostics account for this loss of accuracy and indicate when a single effective state is no longer sufficient. The reduction therefore provides a tractable description of resilience in systems with coexisting pairwise and higher-order interactions. [3] arXiv:2608.14081 [pdf, html, other] Title: Periodic Environmental Forcing Shapes the Stability of Complex Ecological Networks Sayantan Nag Chowdhury Comments: 20 Pages, 8 Figures Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Dynamical Systems (math.DS) Environmental variability is a defining feature of natural ecosystems, yet most theories of ecological stability assume static environments. Here, we develop an analytical theory of stability for complex ecological networks subjected to periodic environmental forcing. We show that, in slowly varying environments, ecosystem stability is determined by the time-averaged rightmost spectral edge of the instantaneous interaction matrix, yielding explicit stability criteria for large ecological communities. The theory predicts a universal hierarchy of resilience across ecological interaction topologies and is validated by numerical simulations. Beyond the adiabatic regime, rapid environmental oscillations dynamically stabilize otherwise unstable ecosystems, revealing a high-frequency rescue effect that is absent from static theories. These results extend ecological stability theory beyond autonomous systems and provide a general framework for understanding resilience in fluctuating environments. [4] arXiv:2608.14108 [pdf, html, other] Title: Spectral stability and slow--fast structure of traveling waves in a regularized sine--Gordon equation Vassilios M Rothos Comments: 22 pages, 11 figures, accept Journal-ref: Wave Motion 2026 Subjects: Pattern Formation and Solitons (nlin.PS); Analysis of PDEs (math.AP); Dynamical Systems (math.DS) We investigate the dynamics and spectral stability of traveling kink and antikink solutions in a dissipative sine--Gordon equation with two distinct fourth--order regularization mechanisms: a mixed space--time (inertial) term and a purely spatial (elliptic) term. The model includes damping, bias forcing, and higher--order dissipative effects, and is motivated by refined descriptions of fluxon dynamics in long Josephson junctions. Using a collective--coordinate reduction, we derive a Melnikov--type condition for speed selection, yielding explicit predictions for asymptotic propagation speeds, which are validated by direct numerical simulations of the full partial differential equation. Spectral stability is analyzed using Evans function techniques adapted to the singular slow--fast structure induced by the regularization. By formulating the linearized problem on a consistent--splitting domain, we show that no additional point spectrum bifurcates from the origin. Near the edges of the essential spectrum, a square--root transformation is used to resolve branch singularities and establish analyticity in a lifted spectral variable. Numerical Evans function computations near $\lambda=0$ and near the essential spectrum edges confirm the analytical results, indicating absence of unstable eigenvalues for both kink and antikink solutions. [5] arXiv:2608.14124 [pdf, other] Title: Adiabatic perturbation theory for the $F=1$ spinor nonlinear Schrödinger equation with nonvanishing boundary conditions Vassilios M Rothos Comments: 31 pages Journal-ref: J. Phys. A: Math. Theor. 59 (2026) 295701 Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Pattern Formation and Solitons (nlin.PS) We develop a systematic adiabatic perturbation theory for the integrable $F=1$ spinor nonlinear Schrödinger equation under nonvanishing boundary conditions, formulated entirely within the framework of the associated Riemann--Hilbert problem. In this setting, localized nonlinear excitations are characterized by discrete spectral data consisting of a complex eigenvalue and an associated polarization vector. For a general class of small perturbations preserving the background, we derive the perturbation-induced evolution of the scattering data directly at the level of the Riemann--Hilbert problem. In the one-soliton sector, this yields a closed finite-dimensional dynamical system governing the slow evolution of the effective soliton parameters, including the spectral variables, the soliton center and phase, the residue amplitude, and the internal polarization state. The latter evolves according to a constrained dynamical equation with no scalar analogue. For localized perturbations, the modulation equations are expressed in explicit integral form in terms of the one-soliton eigenfunctions, providing a fully computable description of the dynamics. In the limit of vanishing boundary conditions, the resulting system reduces to the perturbation theory obtained by E. V. Doktorov, et al, Phys. Rev. A 77 (2008), no. 4, 043617. [6] arXiv:2608.14295 [pdf, html, other] Title: Asynchronous Breathers in Hamiltonian SQUID Metamaterials N. Lazarides Comments: 12 pages, 15 figures Subjects: Pattern Formation and Solitons (nlin.PS) A one-dimensional SQUID (superconducting quantum interference device) array/metamaterial is investigated numerically with respect to its localization properties due to nonlinearity in the absence of dissipation and periodic driving. The system possesses a conserved Hamiltonian function representing its energy, and supports localized modes of the discrete breather type even in the presence of a moderately high dc flux bias. The appearance of discrete breathers in that system has been largely overlooked in literature. We find a new type of discrete breather that is asynchronous, meaning that the frequency of oscillation of the SQUID at the central breather site is different than that of the SQUIDs at the other sites of the metamaterial. Nonlinear localization is investigated by initializing the system with a single-site excitation of given amplitude (initial amplitude) for a fixed value of the coupling coefficient, while parameters such as the dc flux bias, the single-site initial excitation amplitude, and/or the SQUID can vary independently. Using the energetic participation ratio as a measure of the degree of localization, the existence of asynchronous highly localized modes and transitions between delocalized (extended) and localized modes re identified. Cross submissions (showing 7 of 7 entries) [7] arXiv:2608.13743 (cross-list from physics.optics) [pdf, html, other] Title: Nonlinear wave dynamics in photonic time crystals Fabio Biancalana Subjects: Optics (physics.optics); Pattern Formation and Solitons (nlin.PS) Maxwell's wave equation in the presence of a cubic nonlinearity and a periodically time-varying refractive index (a photonic time crystal) is reduced, for spatially monochromatic waves, to a nonlinear Mathieu equation. Near the principal momentum gap this equation admits an autonomous two-dimensional reduction whose complete Hamiltonian phase portrait can be obtained analytically. We derive the two homoclinic separatrices corresponding to temporally localised momentum gap solitons, identify the nonlinear centres and the critical Hamiltonian value $H_c$, and calculate the point of maximum linear parametric gain. We then consider spatially localised pulses and show how the nucleation of multiple spatiotemporal gap solitons can produce a broad supercontinuum in momentum space; for stronger seeds, transient extreme nonlinear localisation can accompany an abrupt additional broadening of this momentum spectrum. These results establish a direct connection between Floquet amplification, nonlinear saturation, homoclinic dynamics, and momentum space spectral broadening in nonlinear photonic time crystals. [8] arXiv:2608.13821 (cross-list from physics.bio-ph) [pdf, html, other] Title: Classification of Intracellular Protein Patterns from Reactive Equilibria Henrik Weyer, Ching Yee Leung, Erwin Frey Comments: 22 pages main text, 17 pages Appendix, 13 figures Subjects: Biological Physics (physics.bio-ph); Soft Condensed Matter (cond-mat.soft); Pattern Formation and Solitons (nlin.PS); Subcellular Processes (q-bio.SC) Self-organized spatial patterns are central to nonequilibrium physics and cell biology, yet locating instabilities in multi-component, reaction-diffusion networks remains challenging because standard eigenvalue analyses scale with the number of biochemical states and rely on reaction kinetics often poorly constrained by experiments. Exploiting the common mass-conserving structure of protein reaction kinetics and the fact that nonlinear feedback …