OOIR: Observatory of International Research

Papers

(The TQCC of Journal of Nonlinear Science is 4. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-03-01 to 2024-03-01.)

Article	Citations
Rogue Waves in the Generalized Derivative Nonlinear Schrödinger Equations	50
Doubly Localized Two-Dimensional Rogue Waves in the Davey–Stewartson I Equation	45
The Complete Classification of Solutions to the Riemann Problem of the Defocusing Complex Modified KdV Equation	40
The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions	38
Stability and Logarithmic Decay of the Solution to Hadamard-Type Fractional Differential Equation	38
Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks	28
Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation	27
Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model	25
Dynamical Behaviors of a Stochastic Food Chain System with Ornstein–Uhlenbeck Process	23
The Blow-Up and Global Existence of Solution to Caputo–Hadamard Fractional Partial Differential Equation with Fractional Laplacian	23
Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain	23
Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation	22
Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates	21
Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics	16
Small Permanent Charge Effects on Individual Fluxes via Poisson–Nernst–Planck Models with Multiple Cations	15
Coexistence, Extinction, and Optimal Harvesting in Discrete-Time Stochastic Population Models	15
Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect	15
The Regularized Visible Fold Revisited	15
2D Euler Equations with Stratonovich Transport Noise as a Large-Scale Stochastic Model Reduction	15
A Geometric Heat-Flow Theory of Lagrangian Coherent Structures	15
Optimal Harvesting of Stochastic Population Models with Periodic Coefficients	14
Vortex Patches Choreography for Active Scalar Equations	13
Stochastic SIR Lévy Jump Model with Heavy-Tailed Increments	13
The Finite-Time Blow-Up for Semilinear Fractional Diffusion Equations with Time $$\psi $$-Caputo Derivative	13
Propagation Speed of the Bistable Traveling Wave to the Lotka–Volterra Competition System in a Periodic Habitat	12

Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics	12
Stationary Distribution, Extinction and Probability Density Function of a Stochastic Vegetation–Water Model in Arid Ecosystems	12
Impact of State-Dependent Dispersal on Disease Prevalence	11
Complex Periodic Bursting Structures in the Rayleigh–van der Pol–Duffing Oscillator	11
Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination	10
A Local-in-Time Theory for Singular SDEs with Applications to Fluid Models with Transport Noise	10
Phase Separation in the Advective Cahn–Hilliard Equation	10
Phytoplankton Competition for Nutrients and Light in a Stratified Lake: A Mathematical Model Connecting Epilimnion and Hypolimnion	10
Spatially Quasi-Periodic Water Waves of Infinite Depth	9
Diffusivity Estimation for Activator–Inhibitor Models: Theory and Application to Intracellular Dynamics of the Actin Cytoskeleton	9
Algebro-Geometric Quasi-Periodic Solutions to the Bogoyavlensky Lattice 2(3) Equations	9
Optimal Decay Estimates for 2D Boussinesq Equations with Partial Dissipation	9
Collapse Versus Blow-Up and Global Existence in the Generalized Constantin–Lax–Majda Equation	9
On the Boussinesq Equations with Non-monotone Temperature Profiles	9
Numerical Study of Zakharov–Kuznetsov Equations in Two Dimensions	9
Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow	9
Periodic Solutions of Stochastic Differential Equations Driven by Lévy Noises	9
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds	9
Stochastic Variational Formulations of Fluid Wave–Current Interaction	9
On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems	9
On the Geometry of Discrete Contact Mechanics	9
Mathematical Framework for Breathing Chimera States	9
Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator	8
Evolution of Dispersal in Advective Patchy Environments	8
Global Regularity for the 2D MHD and Tropical Climate Model with Horizontal Dissipation	8
Sensitivity Analysis for the 2D Navier–Stokes Equations with Applications to Continuous Data Assimilation	8
Perihelion Librations in the Secular Three-Body Problem	8
Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics	8
Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes	8
Elliptic Soliton Solutions: $$\tau $$ Functions, Vertex Operators and Bilinear Identities	8
Rigorous Analysis and Dynamics of Hibler’s Sea Ice Model	7
Linear Instability of Breathers for the Focusing Nonlinear Schrödinger Equation	7
Finite-Data Error Bounds for Koopman-Based Prediction and Control	7
Efficient and Accurate KAM Tori Construction for the Dissipative Spin–Orbit Problem Using a Map Reduction	7
Global Solutions of the Two-Dimensional Kuramoto–Sivashinsky Equation with a Linearly Growing Mode in Each Direction	7
Analysis of a Stochastic Phytoplankton–Zooplankton Model under Non-degenerate and Degenerate Diffusions	7
Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model	7
On Fast–Slow Consensus Networks with a Dynamic Weight	7
Transformation Cloaking in Elastic Plates	7
Relaxation Limit from the Quantum Navier–Stokes Equations to the Quantum Drift–Diffusion Equation	7
Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation	6
Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems	6
Fast-Wave Averaging with Phase Changes: Asymptotics and Application to Moist Atmospheric Dynamics	6
Geometric Control of Two Quadrotors Carrying a Rigid Rod with Elastic Cables	6
An Intrinsic Aggregation Model on the Special Orthogonal Group SO(3): Well-posedness and Collective Behaviours	6
Stability and Sensitivity Analysis of Bird Flapping Flight	6
Well-Posedness of Hibler’s Dynamical Sea-Ice Model	6
On the Motion of Gravity–Capillary Waves with Odd Viscosity	6
From Second-Order Differential Geometry to Stochastic Geometric Mechanics	6
Stability of Elliptic Solutions to the sinh-Gordon Equation	6

Nonintegrability of Nearly Integrable Dynamical Systems Near Resonant Periodic Orbits	6
Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory	5
Stability Against the Odds: The Case of Chromonic Liquid Crystals	5
Localised Radial Patterns on the Free Surface of a Ferrofluid	5
Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in $${\mathbb {R}}^n$$: (I) Under-Damping Case	5
Finite-Dimensionality of Tempered Random Uniform Attractors	5
Rogue Waves and Their Patterns in the Vector Nonlinear Schrödinger Equation	5
Spike-Adding Canard Explosion in a Class of Square-Wave Bursters	5
Scaling Limits for the Generalized Langevin Equation	5
Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy	5
Spontaneous Periodic Orbits in the Navier–Stokes Flow	5
Adaptive Dynamics of a Stoichiometric Phosphorus–Algae–Zooplankton Model with Environmental Fluctuations	5
Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries	5
Reference Configurations Versus Optimal Rotations: A Derivation of Linear Elasticity from Finite Elasticity for all Traction Forces	5
Low-Rank Dynamic Mode Decomposition: An Exact and Tractable Solution	5
The Quasiconvex Envelope of Conformally Invariant Planar Energy Functions in Isotropic Hyperelasticity	5
Turbulent Energy Spectrum via an Interaction Potential	4
Kinetic Equation for Soliton Gas: Integrable Reductions	4
Stability Analysis of Spike Solutions to the Schnakenberg Model with Heterogeneity on Metric Graphs	4
A $${\bar{\partial }}$$-Steepest Descent Method for Oscillatory Riemann–Hilbert Problems	4
Optimal Control, Contact Dynamics and Herglotz Variational Problem	4
Pushed-to-Pulled Front Transitions: Continuation, Speed Scalings, and Hidden Monotonicty	4
Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices	4
Global Bifurcation of Anti-plane Shear Fronts	4
Closed Unstretchable Knotless Ribbons and the Wunderlich Functional	4
Nonlinear Physiologically Structured Population Models with Two Internal Variables	4
Analysis of a Stochastic HBV Infection Model with DNA-Containing Capsids and Virions	4
The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation	4
Analysis of Group of Fish Response to Startle Reaction	4
Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions	4
Relaxation to Fractional Porous Medium Equation from Euler–Riesz System	4
Closed 1/2-Elasticae in the 2-Sphere	4
Remarks on Liouville-Type Theorems for the Steady MHD and Hall-MHD Equations	4
Vortex Pairs and Dipoles on Closed Surfaces	4
Optimal Linear Response for Markov Hilbert–Schmidt Integral Operators and Stochastic Dynamical Systems	4
Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems: A New Approach Using Secants	4
Analysis and Optimal Velocity Control of a Stochastic Convective Cahn–Hilliard Equation	4
On Two Coupled Degenerate Parabolic Equations Motivated by Thermodynamics	4
Disc–Disc Structure in a Two-Species Interacting System on a Flat Torus	4