Nonlinearity

Article	Citations
Existence and regularity results for terminal value problem for nonlinear fractional wave equations	35
Semiclassical states for Choquard type equations with critical growth: critical frequency case *	35
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning	35
Global dynamics of neoclassical growth model with multiple pairs of variable delays	34
Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons	28
Asymptotic spreading speeds for a predator–prey system with two predators and one prey	27
Analysis of a West Nile virus model with nonlocal diffusion and free boundaries	23
Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller–Segel type systems involving signal-dependent motilities?	22
Madelung transform and probability densities in hybrid quantum–classical dynamics	20
Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation	20
Solution landscape of a reduced Landau–de Gennes model on a hexagon	20
Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions	20
Wild pseudohyperbolic attractor in a four-dimensional Lorenz system	19
Well-posedness of the nonlinear Schrödinger equation on the half-plane	19
Influence of a background magnetic field on a 2D magnetohydrodynamic flow	19
Nonradial solutions of nonlinear scalar field equations	19
Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications	18
Stratified equatorial flows in cylindrical coordinates	18
The profile of chiral skyrmions of small radius	17
Stationary shock-like transition fronts in dispersive systems	16
Completely degenerate responsive tori in Hamiltonian systems	16
Global dynamics of a Lotka–Volterra competition patch model*	16
Almost sure invariance principle for random dynamical systems via Gouëzel's approach	16
Singular elliptic problems with unbalanced growth and critical exponent	16
Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves	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
Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock	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
Invariant measures of fractional stochastic delay reaction–diffusion equations on unbounded domains	15
Symmetry structure of multi-dimensional time-fractional partial differential equations	15
The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity	15
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes	14
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
Liquid crystal elastomers wrinkling	12
Hausdorff dimension of an exceptional set in the theory of continued fractions	12
Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds	12
Effects of dispersal and spatial heterogeneity on nonlocal logistic equations	12
Stability and optimal decay for a system of 3D anisotropic Boussinesq equations	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 stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system	11
Singular solutions of the BBM equation: analytical and numerical study	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
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit	11
Relay interlayer synchronisation: invariance and stability 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
Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations	11
Global boundedness of solutions to a parabolic–parabolic chemotaxis system with local sensing in higher dimensions	10
Boundedness for reaction–diffusion systems with Lyapunov functions and intermediate sum conditions	10
On the origins of Riemann–Hilbert problems in mathematics*	10
Spectrality of a class of self-affine measures on R2 *	10
Contour dynamics for surface quasi-geostrophic fronts	10
Bounding extrema over global attractors using polynomial optimisation	10
Homogenization of biomechanical models of plant tissues with randomly distributed cells	10
Rate-induced tipping: thresholds, edge states and connecting orbits	10
Variational approach of critical sharp front speeds in degenerate diffusion model with time delay	10
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations	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
Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems	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
The linear and nonlinear instability of the Akhmediev breather	10
Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model	10
Logarithmic Schrödinger equation with quadratic potential*	10
Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation	10
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
Topological sensitivities via a Lagrangian approach for semilinear problems	9
Regularity results for rough solutions of the incompressible Euler equations via interpolation methods	9

Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks	9
Fourier approximation of the statistical properties of Anosov maps on tori	9
The classical compact groups and Gaussian multiplicative chaos	9
Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations	9
Synchronization of Kuramoto oscillators in dense networks	9
A proof of unlimited multistability for phosphorylation cycles	9
Localized patterns in planar bistable weakly coupled lattice systems	9
Spectral Moran measures on R2 *	9
Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations	9
Bicycle paths, elasticae and sub-Riemannian geometry	9
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case	9
Generating boundary conditions for a Boussinesq system*	9
On omega limiting sets of infinite dimensional Volterra operators	9
Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*	9
Topological Hausdorff dimension of fractal squares and its application to Lipschitz classification	9
Mumford–Shah functionals on graphs and their asymptotics	9
Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case	8
Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam	8
Breather solutions of the cubic Klein–Gordon equation	8
The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation	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
Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems	8
Global solvability and stabilization to a cancer invasion model with remodelling of ECM	8
Integrability, exact reductions and special solutions of the KP–Whitham equations	8
Singularly perturbed boundary-equilibrium bifurcations	8
Algebraic bounds on the Rayleigh–Bénard attractor	8
A predator–prey model with taxis mechanisms and stage structure for the predator	8
Steady incompressible axially symmetric Réthy flows	8
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state	8
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states	8
Global dynamics and travelling waves for a periodic and diffusive chemostat model with two nutrients and one microorganism	8
Well-posedness and global dynamics for the critical Hardy–Sobolev parabolic equation	8
On symmetry of traveling solitary waves for dispersion generalized NLS	8
On the differential geometry of numerical schemes and weak solutions of functional equations	7
Boundary-layer profile of a singularly perturbed nonlocal semi-linear problem arising in chemotaxis	7
Modulated equations of Hamiltonian PDEs and dispersive shocks	7
Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime	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
Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction	7
Turnpike in Lipschitz—nonlinear optimal control	7
On the structure of Hamiltonian impact systems	7
A new type of relaxation oscillation in a model with rate-and-state friction	7
Extreme value distributions of observation recurrences	7
Unique continuation principles for a higher order fractional Laplace equation	7
Existence of a solution to the stochastic nonlocal Cahn–Hilliard Navier–Stokes model via a splitting-up method	7
Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations	7
Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species	7
Typical properties of interval maps preserving the Lebesgue measure *	7
On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity	7
Global multiplicity of solutions for a modified elliptic problem with singular terms *	7
Dynamics of a predator–prey system with nonlinear prey-taxis	7
Genericity of historic behavior for maps and flows	7
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs	7
Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary	7
Scenarios for the creation of hyperchaotic attractors in 3D maps	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
Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds	7
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations	7
Traveling fronts in dissipative granular chains and nonlinear lattices	7
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*	7
Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather	7
Anisotropic (p, q)-equations with gradient dependent reaction	7
ADHM skyrmions	7
Nonlinear stability of fast invading fronts in a Ginzburg–Landau equation with an additional conservation law	6
A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation	6
Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions	6
Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems	6
On topological classification of Morse–Smale diffeomorphisms on the sphere S n (n > 3)	6
A nonlinear quantum adiabatic approximation	6
Transits close to the Lagrangian solutions L 1, L 2 in the elliptic restricted three-body problem	6
The pendulum under vibrations revisited	6
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions *	6
On some rigorous aspects of fragmented condensation	6
The generalized Langevin equation with power-law memory in a nonlinear potential well	6
Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion	6
Effect of driving on coarsening dynamics in phase-separating systems	6
Averaging of dispersion managed nonlinear Schrödinger equations	6

The planar Schrödinger–Poisson system with a positive potential*	6
Local well-posedness of the topological Euler alignment models of collective behavior	6
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method*	6
Semi-classical states for logarithmic Schrödinger equations	6
Derivation of ensemble Kalman–Bucy filters with unbounded nonlinear coefficients	6
Periodic travelling waves on damped 2D lattices with oscillating external forces *	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
On the non-chiral intermediate long wave equation: II. Periodic case	6
Almost flat angles in surface superconductivity	6
Stability and instability of breathers in the U(1) Sasa–Satsuma and nonlinear Schrödinger models*	6
Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics	6
Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps	6
On matrix Painlevé-4 equations	6
Periodic orbits in the Ott–Antonsen manifold	6
Rapidly rotating white dwarfs	6
On existence and uniqueness of a carrying simplex in Kolmogorov differential systems	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
Weighted L 2-contractivity of Langevin dynamics with singular potentials	6
Normalized solutions to p-Laplacian equations with combined nonlinearities*	5
Variational methods for breather solutions of nonlinear wave equations	5
The effect of a positive bound state on the KdV solution: a case study *	5
On mix-norms and the rate of decay of correlations	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 a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach*	5
There are no σ-finite absolutely continuous invariant measures for multicritical circle maps *	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
Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces	5
Global smooth solution of 2D temperature-dependent tropical climate model	5
Hidden spatiotemporal symmetries and intermittency in turbulence	5
Crossing periodic orbits of nonsmooth Liénard systems and applications	5
Stationary multi-kinks in the discrete sine-Gordon equation	5
Upper metric mean dimensions with potential on subsets	5
Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems	5
Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics	5
Stability and bifurcation phenomena in asymptotically Hamiltonian systems	5
On the conservation of energy in two-dimensional incompressible flows	5
On Hölder solutions to the spiral winding problem	5
Exponential moments for disk counting statistics of random normal matrices in the critical regime	5
On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows	5
Super-critical Neumann problems on unbounded domains	5
On the uniqueness of trapezoidal four-body central configurations	5
Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics*	5
The multiplicative constant for the Meijer-G kernel determinant	5
Normalized ground states for the Sobolev critical Schrödinger equation with at least mass critical growth	5
Non-singular Morse–Smale flows on n-manifolds with attractor–repeller dynamics	5
Stability of the planar rarefaction wave to three-dimensional Navier–Stokes–Korteweg equations of compressible fluids	5
On the effect of forcing on fold bifurcations and early-warning signals in population dynamics	5
Mathematical reformulation of the Kolmogorov–Richardson energy cascade in terms of vortex stretching	5
Embedding information onto a dynamical system	5
Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical	5
Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony	5
Inverse variational principles for control systems	5
On the modified fractional Korteweg–de Vries and related equations	5
Extremes and extremal indices for level set observables on hyperbolic systems *	5
Fluid dynamics on logarithmic lattices	5
Area convergence of Voronoi cells on spiral lattices	5
On the fast rotation asymptotics of a non-homogeneous incompressible MHD system	5
Ultradiscrete analogue of the van der Pol equation	5
No solitary waves in 2D gravity and capillary waves in deep water	5
Nonlinear scalar field equation with competing nonlocal terms *	5
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II	5
A probabilistic Takens theorem	5
Soft congestion approximation to the one-dimensional constrained Euler equations	5
Bifurcations of hidden orbits in discontinuous maps	4
Linear encoding of the spatiotemporal cat	4
Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction	4
The r-Hunter–Saxton equation, smooth and singular solutions and their approximation	4
Moments of generalized Cauchy random matrices and continuous-Hahn polynomials	4
Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space	4
Critical sharp front for doubly nonlinear degenerate diffusion equations with time delay	4
Synchronization in adaptive Kuramoto oscillators for power grids with dynamic voltages	4
Superintegrability of Calogero–Moser systems associated with the cyclic quiver	4
Long time finite dimensionality in charged fluids	4
Global attractivity for a nonautonomous Nicholson’s equation with mixed monotonicities	4
Stratified Boussinesq equations with a velocity damping term	4
How close are shell models to the 3D Navier–Stokes equations?	4
Concentration versus absorption for the Vlasov–Navier–Stokes system on bounded domains	4
Vectorial variational problems in L ∞ constrained by the Navier–Stokes equations*	4
Fractional elliptic systems with critical nonlinearities	4
Hyperbolic approximation of the BBM equation	4
Global existence of weak solutions to viscoelastic phase separation part: I. Regular case	4
Piecewise linear maps with heterogeneous chaos	4
Long-time behavior of partially damped systems modeling degenerate plates with piers	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
Two-species competition model with chemotaxis: well-posedness, stability and dynamics	4
Periodic solutions and invariant torus in the Rössler system	4
Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble	4
Torus knot choreographies in the n-body problem	4
Non-reversible processes: GENERIC, hypocoercivity and fluctuations	4
Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces	4
Fractal squares with finitely many connected components *	4