Nonlinearity

Article	Citations
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning	51
Existence and regularity results for terminal value problem for nonlinear fractional wave equations	36
Asymptotic spreading speeds for a predator–prey system with two predators and one prey	31
Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications	24
Solution landscape of a reduced Landau–de Gennes model on a hexagon	24
Wild pseudohyperbolic attractor in a four-dimensional Lorenz system	24
Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth	23
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation	21
Influence of a background magnetic field on a 2D magnetohydrodynamic flow	21
Global dynamics of a Lotka–Volterra competition patch model*	19
Symmetry structure of multi-dimensional time-fractional partial differential equations	19
Invariant measures of fractional stochastic delay reaction–diffusion equations on unbounded domains	18
On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport	17
Rate-induced tipping: thresholds, edge states and connecting orbits	16
Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock	16
Almost sure invariance principle for random dynamical systems via Gouëzel's approach	16
The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity	16
Stability and optimal decay for a system of 3D anisotropic Boussinesq equations	15
Effects of dispersal and spatial heterogeneity on nonlocal logistic equations	15
Global boundedness of solutions to a parabolic–parabolic chemotaxis system with local sensing in higher dimensions	15
On the origins of Riemann–Hilbert problems in mathematics*	15
Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect *	15
Liquid crystal elastomers wrinkling	14
Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds	14
Singular solutions of the BBM equation: analytical and numerical study	14

Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*	14
Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system	14
Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type	13
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit	13
Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations	13
Effects of impulsive harvesting and an evolving domain in a diffusive logistic model*	13
Relay interlayer synchronisation: invariance and stability conditions	13
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations	13
Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations	12
The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential	11
A direct approach to nonuniqueness and failure of compactness for the SQG equation	11
Normalized solutions to p-Laplacian equations with combined nonlinearities*	11
Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds	11
Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations	11
The linear and nonlinear instability of the Akhmediev breather	11
Logarithmic Schrödinger equation with quadratic potential*	11
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*	11
Mathematical analysis of Poisson–Nernst–Planck models with permanent charges and boundary layers: studies on individual fluxes	11
Singularly perturbed boundary-equilibrium bifurcations	11
Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation	11
Modulated equations of Hamiltonian PDEs and dispersive shocks	11
Spectral Moran measures on R2 *	10
Bicycle paths, elasticae and sub-Riemannian geometry	10
Dynamics of a predator–prey system with nonlinear prey-taxis	10
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary	10
Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics	10
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations	10
Spectrality of a class of self-affine measures on R2 *	10
Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model	10
Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime	10
The classical compact groups and Gaussian multiplicative chaos	10
Weighted L 2-contractivity of Langevin dynamics with singular potentials	10
Breather solutions of the cubic Klein–Gordon equation	9
Transits close to the Lagrangian solutions L 1, L 2 in the elliptic restricted three-body problem	9
Upper metric mean dimensions with potential on subsets	9
Well-posedness and global dynamics for the critical Hardy–Sobolev parabolic equation	9
Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case	9
On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity	9
Traveling fronts in dissipative granular chains and nonlinear lattices	9
Mathematical reformulation of the Kolmogorov–Richardson energy cascade in terms of vortex stretching	9
A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation	9
The planar Schrödinger–Poisson system with a positive potential*	9
The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation	9
On the structure of Hamiltonian impact systems	9
The Dirichlet problem for the 1-Laplacian with a general singular term and L 1-data	9
Scenarios for the creation of hyperchaotic attractors in 3D maps	9
Global dynamics of a reaction-diffusion brucellosis model with spatiotemporal heterogeneity and nonlocal delay	8
Normalized multibump solutions to nonlinear Schrödinger equations with steep potential well	8
Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam	8
On spectral structure and spectral eigenvalue problems for a class of self similar spectral measure with product form	8

Global multiplicity of solutions for a modified elliptic problem with singular terms *	8
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs	8
Global weak solutions to a Navier–Stokes–Cahn–Hilliard system with chemotaxis and singular potential	8
Algebraic bounds on the Rayleigh–Bénard attractor	8
Almost flat angles in surface superconductivity	8
Extreme first passage times of piecewise deterministic Markov processes	8
Doubly nonlinear Schrödinger ground states on metric graphs	8
Normalized solutions of L 2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities	8
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*	8
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions *	8
ADHM skyrmions	8
Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion	8
Extremes and extremal indices for level set observables on hyperbolic systems *	8
On topological classification of Morse–Smale diffeomorphisms on the sphere S n (n > 3)	8
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state	8
Semi-classical states for logarithmic Schrödinger equations	8
Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction	8
Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity	8
Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical	8
Piecewise linear maps with heterogeneous chaos	7
Bowen’s equations for upper metric mean dimension with potential	7
On the modified fractional Korteweg–de Vries and related equations	7
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method*	7
Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems	7
Genericity of historic behavior for maps and flows	7
Extreme value distributions of observation recurrences	7
On the non-chiral intermediate long wave equation: II. Periodic case	7
Averaging of dispersion managed nonlinear Schrödinger equations	7
Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations	7
Moments of generalized Cauchy random matrices and continuous-Hahn polynomials	7
Anisotropic (p, q)-equations with gradient dependent reaction	7
Embedding information onto a dynamical system	7
‘Life after death’ in ordinary differential equations with a non-Lipschitz singularity	7
Finite-time blow-up and boundedness in a 2D Keller–Segel system with rotation	7
Fluid dynamics on logarithmic lattices	7
Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems	7
Periodic orbits in the Ott–Antonsen manifold	7
On existence and uniqueness of a carrying simplex in Kolmogorov differential systems	7
Turnpike in Lipschitz—nonlinear optimal control	7
Stability of the multi-solitons of the modified Korteweg–de Vries equation *	7
Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony	6
Exponential moments for disk counting statistics of random normal matrices in the critical regime	6
Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction	6
Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter	6
Global attractivity for a nonautonomous Nicholson’s equation with mixed monotonicities	6
Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions	6
Response solutions to the quasi-periodically forced systems with degenerate equilibrium: a simple proof of a result of W Si and J Si and extensions	6
Two-species competition model with chemotaxis: well-posedness, stability and dynamics	6
Non-singular Morse–Smale flows on n-manifolds with attractor–repeller dynamics	6
Hyperbolic approximation of the BBM equation	6
Derivation of ensemble Kalman–Bucy filters with unbounded nonlinear coefficients	6
On mix-norms and the rate of decay of correlations	6
Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems	6
Linear encoding of the spatiotemporal cat	6
Hidden spatiotemporal symmetries and intermittency in turbulence	6
Inverse variational principles for control systems	6
Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law	6
Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles	6
On matrix Painlevé-4 equations	6
Torus knot choreographies in the n-body problem	6
Gevrey stability of hydrostatic approximate for the Navier–Stokes equations in a thin domain	6
Critical sharp front for doubly nonlinear degenerate diffusion equations with time delay	6
The pendulum under vibrations revisited	6
Classical n-body scattering with long-range potentials	6
On some rigorous aspects of fragmented condensation	6
Stability and instability of breathers in the U(1) Sasa–Satsuma and nonlinear Schrödinger models*	6
Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces	6
The Boussinesq system revisited	6
Evolution of cooperation under the coexistence of imitation and aspiration dynamics in structured populations	6
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system	6
Vectorial variational problems in L ∞ constrained by the Navier–Stokes equations*	6
On the effect of forcing on fold bifurcations and early-warning signals in population dynamics	6
Stability of the planar rarefaction wave to three-dimensional Navier–Stokes–Korteweg equations of compressible fluids	6
Spectrality of random convolutions generated by finitely many Hadamard triples	5
Area convergence of Voronoi cells on spiral lattices	5
Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps	5
Long-time behavior of partially damped systems modeling degenerate plates with piers	5
On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation	5
A multiple time renewal equation for neural assemblies with elapsed time model	5
Global existence and decay estimates of solutions to the MHD–Boussinesq system with stratification effects*	5

The multiplicative constant for the Meijer-G kernel determinant	5
On Hölder solutions to the spiral winding problem	5
Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales	5
Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: two-scale expansions and symmetrisations	5
Periodic travelling waves on damped 2D lattices with oscillating external forces *	5
Variational methods for breather solutions of nonlinear wave equations	5
Hausdorff dimension of thin higher-dimensional solenoidal attractors	5
Unstable entropies and dimension theory of partially hyperbolic systems	5
Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics*	5
Ultradiscrete analogue of the van der Pol equation	5
Learning strange attractors with reservoir systems	5
Synchronisation conditions in the Kuramoto model and their relationship to seminorms	5
On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems*	5
On global smooth solutions of the 3D spherically symmetric Euler equations with time-dependent damping and physical vacuum	5
On the non-chiral intermediate long wave equation	5
Stationary multi-kinks in the discrete sine-Gordon equation	5
Global smooth solution of 2D temperature-dependent tropical climate model	5
Global existence of weak solutions to viscoelastic phase separation part: I. Regular case	5
On the conservation of energy in two-dimensional incompressible flows	5
Bifurcations of hidden orbits in discontinuous maps	5
Nonlinear scalar field equation with competing nonlocal terms *	5
The effect of a positive bound state on the KdV solution: a case study *	5
There are no σ-finite absolutely continuous invariant measures for multicritical circle maps *	5
Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems *	5
On backward attractors of interval maps*	5
Concentration versus absorption for the Vlasov–Navier–Stokes system on bounded domains	5
On a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach*	5
Fractional elliptic systems with critical nonlinearities	5
On the uniqueness of trapezoidal four-body central configurations	5
Soft congestion approximation to the one-dimensional constrained Euler equations	5
Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics	5
Long time finite dimensionality in charged fluids	5
Recursion and Hamiltonian operators for integrable nonabelian difference equations	4
Approximate localised dihedral patterns near a turing instability	4
Simple two-layer dispersive models in the Hamiltonian reduction formalism	4
Spatially discrete Boussinesq equation: integrability, Darboux transformation, exact solutions and continuum limit	4
The stability of the b-family of peakon equations	4
Contact topology and non-equilibrium thermodynamics	4
Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction	4
Exponential stability estimate for the derivative nonlinear Schrödinger equation*	4
Generalized Hardy operators	4
Linear response for the dynamic Laplacian and finite-time coherent sets	4
The p-Laplacian in thin channels with locally periodic roughness and different scales*	4
How close are shell models to the 3D Navier–Stokes equations?	4
A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis	4
Approximating the ground state eigenvalue via the effective potential	4
Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates	4
Well-posedness and applications of classical elastohydrodynamics for a swimming filament	4
Asymptotic stability of viscous shocks in the modular Burgers equation	4
Asymptotics for the second-largest Lyapunov exponent for some Perron–Frobenius operator cocycles	4
Non-reversible processes: GENERIC, hypocoercivity and fluctuations	4
Spectral stability of pattern-forming fronts in the complex Ginzburg–Landau equation with a quenching mechanism	4
Optimal time decay of the compressible Navier–Stokes equations for a reacting mixture	4
Superintegrability of Calogero–Moser systems associated with the cyclic quiver	4
Multiple timescales and the parametrisation method in geometric singular perturbation theory	4
Fractal squares with finitely many connected components *	4
Computability of topological pressure on compact shift spaces beyond finite type*	4
Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations	4
Internal ring waves in a three-layer fluid on a current with a constant vertical shear	4
On a fluid–structure interaction problem for plaque growth	4
Diffusive spatial movement with memory in an advective environment	4
Gap sequences and Topological properties of Bedford–McMullen sets*	4
Quasilinear Schrödinger equations involving singular potentials	4
Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble	4
Passivity of Lotka–Volterra and quasi-polynomial systems	4
Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession*	4
The initial-boundary value problem for the Lifshitz–Slyozov equation with non-smooth rates at the boundary	4
Uniform regularity estimates and inviscid limit for the compressible non-resistive magnetohydrodynamics system	4
Landau-like theory for buckling phenomena and its application to the elastica hypoarealis	4
Dynamically defined subsets of generic self-affine sets*	4
Analysis of travelling waves and propagating supports for a nonlinear model of flame propagation with a p-Laplacian operator and advection	4
A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa–Holm system	4
Weak–strong uniqueness property for models of compressible viscous fluids near vacuum*	4
Long time well-posedness of Whitham–Boussinesq systems	4
Stability and bifurcation phenomena in asymptotically Hamiltonian systems	4
Three-dimensional shear driven turbulence with noise at the boundary	4
Stratified Boussinesq equations with a velocity damping term	4
Growing patterns	4
Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator	4
KdV on an incoming tide	4
Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations	4
Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems*	4
Spatio-temporal dynamics of a model for the effect of variable ages at reproduction	4
Compressible Navier–Stokes equations with heterogeneous pressure laws	4
Flexibility and rigidity of free boundary MHD equilibria	4
Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity	4
On the global attractivity of non-autonomous neural networks with a distributed delay	4