Nonlinearity

Article	Citations
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning	38
Semiclassical states for Choquard type equations with critical growth: critical frequency case *	36
Existence and regularity results for terminal value problem for nonlinear fractional wave equations	35
Global dynamics of neoclassical growth model with multiple pairs of variable delays	34
Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons	30
Asymptotic spreading speeds for a predator–prey system with two predators and one prey	28
Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller–Segel type systems involving signal-dependent motilities?	23
Analysis of a West Nile virus model with nonlocal diffusion and free boundaries	23
Solution landscape of a reduced Landau–de Gennes model on a hexagon	22
Madelung transform and probability densities in hybrid quantum–classical dynamics	20
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation	20
Wild pseudohyperbolic attractor in a four-dimensional Lorenz system	20
Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions	20
Well-posedness of the nonlinear Schrödinger equation on the half-plane	20
Influence of a background magnetic field on a 2D magnetohydrodynamic flow	19
Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications	19
Stratified equatorial flows in cylindrical coordinates	19
Nonradial solutions of nonlinear scalar field equations	19
Symmetry structure of multi-dimensional time-fractional partial differential equations	17
The profile of chiral skyrmions of small radius	17
Singular elliptic problems with unbalanced growth and critical exponent	17
Global dynamics of a Lotka–Volterra competition patch model*	17
Stationary shock-like transition fronts in dispersive systems	16
Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock	16
Completely degenerate responsive tori in Hamiltonian systems	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
Invariant measures of fractional stochastic delay reaction–diffusion equations on unbounded domains	16
On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport	16
Global existence and blow-up of solutions to a nonlocal Kirchhoff diffusion problem	15
Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves	15
Limit theorems for some time-dependent expanding dynamical systems	15
Existence of noise induced order, a computer aided proof	15
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes	14
Stability and optimal decay for a system of 3D anisotropic Boussinesq equations	14
Relay interlayer synchronisation: invariance and stability conditions	12
Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds	12
Effects of dispersal and spatial heterogeneity on nonlocal logistic equations	12
Effects of impulsive harvesting and an evolving domain in a diffusive logistic model*	12
The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations	12
Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*	12
Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations	12
Liquid crystal elastomers wrinkling	12
Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations	12
Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect *	12
Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type	12
Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions	11
On the origins of Riemann–Hilbert problems in mathematics*	11
Synchronization of Kuramoto oscillators in dense networks	11
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit	11
Boundedness for reaction–diffusion systems with Lyapunov functions and intermediate sum conditions	11
Contour dynamics for surface quasi-geostrophic fronts	11
Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system	11
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed	11
Variational approach of critical sharp front speeds in degenerate diffusion model with time delay	11
Single-point blow-up in the Cauchy problem for the higher-dimensional Keller–Segel system	11
Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth	11
Singular solutions of the BBM equation: analytical and numerical study	11
Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers	10
Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification	10
Global boundedness of solutions to a parabolic–parabolic chemotaxis system with local sensing in higher dimensions	10
Mumford–Shah functionals on graphs and their asymptotics	10
Mathematical analysis of Poisson–Nernst–Planck models with permanent charges and boundary layers: studies on individual fluxes	10
Spectrality of a class of self-affine measures on R2 *	10
Logarithmic Schrödinger equation with quadratic potential*	10
Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation	10
Spectral Moran measures on R2 *	10
Homogenization of biomechanical models of plant tissues with randomly distributed cells	10
Dynamics of a chemostat with periodic nutrient supply and delay in the growth	10
A direct approach to nonuniqueness and failure of compactness for the SQG equation	10
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations	10
Bounding extrema over global attractors using polynomial optimisation	10
Topological sensitivities via a Lagrangian approach for semilinear problems	10
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*	10
The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential	10

Rate-induced tipping: thresholds, edge states and connecting orbits	10
The linear and nonlinear instability of the Akhmediev breather	10
Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model	10
Fourier approximation of the statistical properties of Anosov maps on tori	9
Bicycle paths, elasticae and sub-Riemannian geometry	9
The Dirichlet problem for the 1-Laplacian with a general singular term and L 1-data	9
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case	9
On omega limiting sets of infinite dimensional Volterra operators	9
The classical compact groups and Gaussian multiplicative chaos	9
Global dynamics and travelling waves for a periodic and diffusive chemostat model with two nutrients and one microorganism	9
Generating boundary conditions for a Boussinesq system*	9
Regularity results for rough solutions of the incompressible Euler equations via interpolation methods	9
Localized patterns in planar bistable weakly coupled lattice systems	9
Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations	9
Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations	9
A proof of unlimited multistability for phosphorylation cycles	9
Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis	8
A predator–prey model with taxis mechanisms and stage structure for the predator	8
Steady incompressible axially symmetric Réthy flows	8
Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam	8
Integrability, exact reductions and special solutions of the KP–Whitham equations	8
The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation	8
Dynamics of a predator–prey system with nonlinear prey-taxis	8
Global weak solutions to a Navier–Stokes–Cahn–Hilliard system with chemotaxis and singular potential	8
Existence of a solution to the stochastic nonlocal Cahn–Hilliard Navier–Stokes model via a splitting-up method	8
Global solvability and stabilization to a cancer invasion model with remodelling of ECM	8
Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime	8
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state	8
Singularly perturbed boundary-equilibrium bifurcations	8
Well-posedness and global dynamics for the critical Hardy–Sobolev parabolic equation	8
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary	8
Scenarios for the creation of hyperchaotic attractors in 3D maps	8
Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks	8
Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case	8
Breather solutions of the cubic Klein–Gordon equation	8
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states	8
Traveling fronts in dissipative granular chains and nonlinear lattices	8
Algebraic bounds on the Rayleigh–Bénard attractor	8
Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather	7
Mathematical reformulation of the Kolmogorov–Richardson energy cascade in terms of vortex stretching	7
ADHM skyrmions	7
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions *	7
Unique continuation principles for a higher order fractional Laplace equation	7
The planar Schrödinger–Poisson system with a positive potential*	7
Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species	7
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations*	7
Sharp time decay rates of H 1 weak solutions for the 2D MHD equations with linear damping velocity	7
Turnpike in Lipschitz—nonlinear optimal control	7
Global multiplicity of solutions for a modified elliptic problem with singular terms *	7
On the structure of Hamiltonian impact systems	7
A probabilistic Takens theorem	7
Extreme value distributions of observation recurrences	7
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs	7
Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics	7
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects	7
Extreme first passage times of piecewise deterministic Markov processes	7
Typical properties of interval maps preserving the Lebesgue measure *	7
On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity	7
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations	7
Anisotropic (p, q)-equations with gradient dependent reaction	7
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*	7
Genericity of historic behavior for maps and flows	7
Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction	7
On the differential geometry of numerical schemes and weak solutions of functional equations	7
A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation	7
Modulated equations of Hamiltonian PDEs and dispersive shocks	7
Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations	7
Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds	7
Semi-classical states for logarithmic Schrödinger equations	7
Transits close to the Lagrangian solutions L 1, L 2 in the elliptic restricted three-body problem	7
Normalized solutions to p-Laplacian equations with combined nonlinearities*	7
Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps	6
Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical	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
Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law	6
Effect of driving on coarsening dynamics in phase-separating systems	6
Local well-posedness of the topological Euler alignment models of collective behavior	6
On topological classification of Morse–Smale diffeomorphisms on the sphere S n (n > 3)	6
Normalized solutions of L 2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities	6

Derivation of ensemble Kalman–Bucy filters with unbounded nonlinear coefficients	6
Averaging of dispersion managed nonlinear Schrödinger equations	6
Upper metric mean dimensions with potential on subsets	6
On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows	6
Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data	6
Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity	6
Stability of the multi-solitons of the modified Korteweg–de Vries equation *	6
Extremes and extremal indices for level set observables on hyperbolic systems *	6
Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion	6
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method*	6
A nonlinear quantum adiabatic approximation	6
Rapidly rotating white dwarfs	6
On existence and uniqueness of a carrying simplex in Kolmogorov differential systems	6
On the modified fractional Korteweg–de Vries and related equations	6
Periodic travelling waves on damped 2D lattices with oscillating external forces *	6
Bowen’s equations for upper metric mean dimension with potential	6
Weighted L 2-contractivity of Langevin dynamics with singular potentials	6
‘Life after death’ in ordinary differential equations with a non-Lipschitz singularity	6
Long-time behavior of partially damped systems modeling degenerate plates with piers	6
On the non-chiral intermediate long wave equation: II. Periodic case	6
Almost flat angles in surface superconductivity	6
On matrix Painlevé-4 equations	6
Periodic orbits in the Ott–Antonsen manifold	6
The r-Hunter–Saxton equation, smooth and singular solutions and their approximation	6
Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems	6
Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems	6
Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions	6
The pendulum under vibrations revisited	6
Crossing periodic orbits of nonsmooth Liénard systems and applications	5
Soft congestion approximation to the one-dimensional constrained Euler equations	5
Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics	5
On mix-norms and the rate of decay of correlations	5
Variational methods for breather solutions of nonlinear wave equations	5
Embedding information onto a dynamical system	5
Fluid dynamics on logarithmic lattices	5
Super-critical Neumann problems on unbounded domains	5
Ultradiscrete analogue of the van der Pol equation	5
Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics	5
Hidden spatiotemporal symmetries and intermittency in turbulence	5
Global smooth solution of 2D temperature-dependent tropical climate model	5
On spectral structure and spectral eigenvalue problems for a class of self similar spectral measure with product form	5
Non-singular Morse–Smale flows on n-manifolds with attractor–repeller dynamics	5
The multiplicative constant for the Meijer-G kernel determinant	5
On the effect of forcing on fold bifurcations and early-warning signals in population dynamics	5
Long time finite dimensionality in charged fluids	5
On the conservation of energy in two-dimensional incompressible flows	5
Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems	5
Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles	5
Finite-time blow-up and boundedness in a 2D Keller–Segel system with rotation	5
On Hölder solutions to the spiral winding problem	5
Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces	5
Nonlinear scalar field equation with competing nonlocal terms *	5
Doubly nonlinear Schrödinger ground states on metric graphs	5
The effect of a positive bound state on the KdV solution: a case study *	5
On the uniqueness of trapezoidal four-body central configurations	5
Moments of generalized Cauchy random matrices and continuous-Hahn polynomials	5
No solitary waves in 2D gravity and capillary waves in deep water	5
Stationary multi-kinks in the discrete sine-Gordon equation	5
Stability of the planar rarefaction wave to three-dimensional Navier–Stokes–Korteweg equations of compressible fluids	5
Piecewise linear maps with heterogeneous chaos	5
Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony	5
Exponential moments for disk counting statistics of random normal matrices in the critical regime	5
Inverse variational principles for control systems	5
There are no σ-finite absolutely continuous invariant measures for multicritical circle maps *	5
Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics*	5
On a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach*	5
Area convergence of Voronoi cells on spiral lattices	5
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system	5
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	5
Two-species competition model with chemotaxis: well-posedness, stability and dynamics	5
Synchronization in adaptive Kuramoto oscillators for power grids with dynamic voltages	4
Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces	4
KdV on an incoming tide	4
Global attractivity for a nonautonomous Nicholson’s equation with mixed monotonicities	4
Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations	4
How close are shell models to the 3D Navier–Stokes equations?	4
Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space	4
Torus knot choreographies in the n-body problem	4
Hyperbolic approximation of the BBM equation	4
Global existence of weak solutions to viscoelastic phase separation part: I. Regular case	4
Superintegrability of Calogero–Moser systems associated with the cyclic quiver	4
Unstable entropies and dimension theory of partially hyperbolic systems	4
Normalized multibump solutions to nonlinear Schrödinger equations with steep potential well	4
Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction	4
A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis	4
Gevrey stability of hydrostatic approximate for the Navier–Stokes equations in a thin domain	4
Non-reversible processes: GENERIC, hypocoercivity and fluctuations	4
Stability and bifurcation phenomena in asymptotically Hamiltonian systems	4
Fractal squares with finitely many connected components *	4
Bifurcations of hidden orbits in discontinuous maps	4
Linear encoding of the spatiotemporal cat	4
Stratified Boussinesq equations with a velocity damping term	4
Periodic solutions and invariant torus in the Rössler system	4
Fractional elliptic systems with critical nonlinearities	4
Critical sharp front for doubly nonlinear degenerate diffusion equations with time delay	4