Nonlinearity

Article	Citations
Existence and regularity results for terminal value problem for nonlinear fractional wave equations	38
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning	35
Semiclassical states for Choquard type equations with critical growth: critical frequency case *	34
Global dynamics of neoclassical growth model with multiple pairs of variable delays	33
Asymptotic spreading speeds for a predator–prey system with two predators and one prey	27
Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons	26
Modeling shallow water waves	23
Analysis of a West Nile virus model with nonlocal diffusion and free boundaries	22
Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller–Segel type systems involving signal-dependent motilities?	20
Solution landscape of a reduced Landau–de Gennes model on a hexagon	20
Two-stroke relaxation oscillators	20
Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions	20
Madelung transform and probability densities in hybrid quantum–classical dynamics	19
Wild pseudohyperbolic attractor in a four-dimensional Lorenz system	18
Nonradial solutions of nonlinear scalar field equations	18
Influence of a background magnetic field on a 2D magnetohydrodynamic flow	18
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation	18
Stratified equatorial flows in cylindrical coordinates	18
Well-posedness of the nonlinear Schrödinger equation on the half-plane	18
The profile of chiral skyrmions of small radius	17
Global dynamics of a Lotka–Volterra competition patch model*	17
On the Euler-alignment system with weakly singular communication weights	16
Singular elliptic problems with unbalanced growth and critical exponent	16
Almost sure invariance principle for random dynamical systems via Gouëzel's approach	16
Completely degenerate responsive tori in Hamiltonian systems	16

Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves	15
Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications	15
The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity	15
Stationary shock-like transition fronts in dispersive systems	15
Global existence and blow-up of solutions to a nonlocal Kirchhoff diffusion problem	15
Limit theorems for some time-dependent expanding dynamical systems	15
Existence of noise induced order, a computer aided proof	15
On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport	15
Symmetry structure of multi-dimensional time-fractional partial differential equations	14
Invariant measures of fractional stochastic delay reaction–diffusion equations on unbounded domains	14
Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock	14
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes	14
Blow-up profiles in quasilinear fully parabolic Keller–Segel systems	13
New variational characterization of periodic waves in the fractional Korteweg–de Vries equation	13
The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations	12
Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type	12
Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*	12
Liquid crystal elastomers wrinkling	12
Stability and optimal decay for a system of 3D anisotropic Boussinesq equations	12
Effects of dispersal and spatial heterogeneity on nonlocal logistic equations	12
Hausdorff dimension of an exceptional set in the theory of continued fractions	11
Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations	11
Global existence of weak solutions for Navier–Stokes-BGK system	11
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit	11
Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations	11
Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions	11
Single-point blow-up in the Cauchy problem for the higher-dimensional Keller–Segel system	11
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed	11
Relay interlayer synchronisation: invariance and stability conditions	11
Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect *	11
Singular solutions of the BBM equation: analytical and numerical study	11
On the origins of Riemann–Hilbert problems in mathematics*	10
The linear and nonlinear instability of the Akhmediev breather	10
Bounding extrema over global attractors using polynomial optimisation	10
Homogenization of biomechanical models of plant tissues with randomly distributed cells	10
Boundedness for reaction–diffusion systems with Lyapunov functions and intermediate sum conditions	10
Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D	10
Effects of impulsive harvesting and an evolving domain in a diffusive logistic model*	10
Micropolar meets Newtonian in 3D. The Rayleigh–Bénard problem for large Prandtl numbers	10
The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential	10
Dynamics of a chemostat with periodic nutrient supply and delay in the growth	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
Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems	10
Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds	10
Spectral Moran measures on R2 *	9
On omega limiting sets of infinite dimensional Volterra operators	9
Fourier approximation of the statistical properties of Anosov maps on tori	9
Localized patterns in planar bistable weakly coupled lattice systems	9

Mumford–Shah functionals on graphs and their asymptotics	9
Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations	9
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations	9
Generating boundary conditions for a Boussinesq system*	9
Topological sensitivities via a Lagrangian approach for semilinear problems	9
Regularity results for rough solutions of the incompressible Euler equations via interpolation methods	9
Global boundedness of solutions to a parabolic–parabolic chemotaxis system with local sensing in higher dimensions	9
Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations	9
Variational approach of critical sharp front speeds in degenerate diffusion model with time delay	9
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case	9
Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model	9
Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system	9
Large time dynamics of 2D semi-dissipative Boussinesq equations	9
Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification	9
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*	9
The classical compact groups and Gaussian multiplicative chaos	9
A direct approach to nonuniqueness and failure of compactness for the SQG equation	9
Mathematical analysis of Poisson–Nernst–Planck models with permanent charges and boundary layers: studies on individual fluxes	9
Synchronization of Kuramoto oscillators in dense networks	9
A proof of unlimited multistability for phosphorylation cycles	9
Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks	8
Steady incompressible axially symmetric Réthy flows	8
Integrability, exact reductions and special solutions of the KP–Whitham equations	8
Bicycle paths, elasticae and sub-Riemannian geometry	8
Global dynamics and travelling waves for a periodic and diffusive chemostat model with two nutrients and one microorganism	8
On symmetry of traveling solitary waves for dispersion generalized NLS	8
Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems	8
Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam	8
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states	8
The Dirichlet problem for the 1-Laplacian with a general singular term and L 1-data	8
Global weak solutions to a Navier–Stokes–Cahn–Hilliard system with chemotaxis and singular potential	8
A predator–prey model with taxis mechanisms and stage structure for the predator	8
Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case	8
Global solvability and stabilization to a cancer invasion model with remodelling of ECM	8
The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation	8
Singularity formation and global Well-posedness for the generalized Constantin–Lax–Majda equation with dissipation	8
Contour dynamics for surface quasi-geostrophic fronts	8
Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction	7
Anisotropic (p, q)-equations with gradient dependent reaction	7
A new type of relaxation oscillation in a model with rate-and-state friction	7
ADHM skyrmions	7
Extreme value distributions of observation recurrences	7
Extreme first passage times of piecewise deterministic Markov processes	7
Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime	7
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state	7
Sharp time decay rates of H 1 weak solutions for the 2D MHD equations with linear damping velocity	7
Global multiplicity of solutions for a modified elliptic problem with singular terms *	7
Traveling fronts in dissipative granular chains and nonlinear lattices	7
Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather	7
Algebraic bounds on the Rayleigh–Bénard attractor	7
Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups	7
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects	7
On numerical inverse scattering for the Korteweg–de Vries equation with discontinuous step-like data	7
Breather solutions of the cubic Klein–Gordon equation	7
Typical properties of interval maps preserving the Lebesgue measure *	7
Slow travelling wave solutions of the nonlocal Fisher-KPP equation	7
On the structure of Hamiltonian impact systems	7
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*	7
Genericity of historic behavior for maps and flows	7
Well-posedness and global dynamics for the critical Hardy–Sobolev parabolic equation	7
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary	7
Existence of a solution to the stochastic nonlocal Cahn–Hilliard Navier–Stokes model via a splitting-up method	7
Modulated equations of Hamiltonian PDEs and dispersive shocks	7
Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations	7
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations*	7
On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity	7
Rate-induced tipping: thresholds, edge states and connecting orbits	7
On existence and uniqueness of a carrying simplex in Kolmogorov differential systems	6
Periodic travelling waves on damped 2D lattices with oscillating external forces *	6
On some rigorous aspects of fragmented condensation	6
Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law	6
Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis	6
Effect of driving on coarsening dynamics in phase-separating systems	6
Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics	6
The planar Schrödinger–Poisson system with a positive potential*	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
Likely cavitation and radial motion of stochastic elastic spheres	6
Dynamics of a predator–prey system with nonlinear prey-taxis	6
Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data	6

‘Life after death’ in ordinary differential equations with a non-Lipschitz singularity	6
Stability of the multi-solitons of the modified Korteweg–de Vries equation *	6
Scenarios for the creation of hyperchaotic attractors in 3D maps	6
Stability and instability of breathers in the U(1) Sasa–Satsuma and nonlinear Schrödinger models*	6
Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion	6
Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems	6
Averaging of dispersion managed nonlinear Schrödinger equations	6
Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species	6
Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds	6
Semi-classical states for logarithmic Schrödinger equations	6
The pendulum under vibrations revisited	6
Derivation of ensemble Kalman–Bucy filters with unbounded nonlinear coefficients	6
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs	6
The generalized Langevin equation with power-law memory in a nonlinear potential well	6
Almost flat angles in surface superconductivity	6
Unique continuation principles for a higher order fractional Laplace equation	6
Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions	6
Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps	6
On matrix Painlevé-4 equations	6
A nonlinear quantum adiabatic approximation	6
Singularly perturbed boundary-equilibrium bifurcations	6
Periodic orbits in the Ott–Antonsen manifold	5
Ultradiscrete analogue of the van der Pol equation	5
The multiplicative constant for the Meijer-G kernel determinant	5
On the non-chiral intermediate long wave equation: II. Periodic case	5
Rapidly rotating white dwarfs	5
Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces	5
Spiral Delone sets and three distance theorem	5
Stationary multi-kinks in the discrete sine-Gordon equation	5
Turnpike in Lipschitz—nonlinear optimal control	5
Transits close to the Lagrangian solutions L 1, L 2 in the elliptic restricted three-body problem	5
On the modified fractional Korteweg–de Vries and related equations	5
On the conservation of energy in two-dimensional incompressible flows	5
On a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach*	5
Exponential moments for disk counting statistics of random normal matrices in the critical regime	5
Fluid dynamics on logarithmic lattices	5
Weighted L 2-contractivity of Langevin dynamics with singular potentials	5
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system	5
Super-critical Neumann problems on unbounded domains	5
Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: two-scale expansions and symmetrisations	5
Area convergence of Voronoi cells on spiral lattices	5
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations	5
The effect of a positive bound state on the KdV solution: a case study *	5
No solitary waves in 2D gravity and capillary waves in deep water	5
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II	5
Mathematical reformulation of the Kolmogorov–Richardson energy cascade in terms of vortex stretching	5
Upper metric mean dimensions with potential on subsets	5
On the effect of forcing on fold bifurcations and early-warning signals in population dynamics	5
Inverse variational principles for control systems	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
On the differential geometry of numerical schemes and weak solutions of functional equations	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
Global weak solutions to fully cross-diffusive systems with nonlinear diffusion and saturated taxis sensitivity	5
Global smooth solution of 2D temperature-dependent tropical climate model	5
Extremes and extremal indices for level set observables on hyperbolic systems *	5
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method*	5
A Bendixon–Dulac theorem for some piecewise systems	5
Non-singular Morse–Smale flows on n-manifolds with attractor–repeller dynamics	5
There are no σ-finite absolutely continuous invariant measures for multicritical circle maps *	5
Threshold for blowup for the supercritical cubic wave equation	5
Crossing periodic orbits of nonsmooth Liénard systems and applications	5
Normalized solutions to p-Laplacian equations with combined nonlinearities*	5
Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems	5
On Hölder solutions to the spiral winding problem	5
Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics	5
On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows	5
On mix-norms and the rate of decay of correlations	5
New effective pressure and existence of global strong solution for compressible Navier–Stokes equations with general viscosity coefficient in one dimension	5
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions *	5
On the uniqueness of trapezoidal four-body central configurations	5
Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics*	5
Non-reversible processes: GENERIC, hypocoercivity and fluctuations	4
Piecewise linear maps with heterogeneous chaos	4
Long time finite dimensionality in charged fluids	4
Stability and bifurcation phenomena in asymptotically Hamiltonian systems	4
A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation	4
Long-time behavior of partially damped systems modeling degenerate plates with piers	4
Hidden spatiotemporal symmetries and intermittency in turbulence	4
A probabilistic Takens theorem	4
Global existence of weak solutions to viscoelastic phase separation part: I. Regular case	4
Fractal squares with finitely many connected components *	4
Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony	4
Global attractivity for a nonautonomous Nicholson’s equation with mixed monotonicities	4
Bifurcations of hidden orbits in discontinuous maps	4
Linear encoding of the spatiotemporal cat	4
How close are shell models to the 3D Navier–Stokes equations?	4
Synchronization in adaptive Kuramoto oscillators for power grids with dynamic voltages	4
Superintegrability of Calogero–Moser systems associated with the cyclic quiver	4
Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical	4
Embedding information onto a dynamical system	4
Finite-time blow-up and boundedness in a 2D Keller–Segel system with rotation	4
Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations	4
Nonlinear scalar field equation with competing nonlocal terms *	4
Hyperbolic approximation of the BBM equation	4