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 2020-05-01 to 2024-05-01.)

Article	Citations
Rogue Waves in the Generalized Derivative Nonlinear Schrödinger Equations	51
Doubly Localized Two-Dimensional Rogue Waves in the Davey–Stewartson I Equation	46
The Complete Classification of Solutions to the Riemann Problem of the Defocusing Complex Modified KdV Equation	43
The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions	41
Stability and Logarithmic Decay of the Solution to Hadamard-Type Fractional Differential Equation	40
Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks	31
Pattern Transformation in Higher-Order Lumps of the Kadomtsev–Petviashvili I Equation	29
Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain	26
The Blow-Up and Global Existence of Solution to Caputo–Hadamard Fractional Partial Differential Equation with Fractional Laplacian	25
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	25
Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates	24
Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation	24
Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect	17
Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics	16
Coexistence, Extinction, and Optimal Harvesting in Discrete-Time Stochastic Population Models	16
Small Permanent Charge Effects on Individual Fluxes via Poisson–Nernst–Planck Models with Multiple Cations	16
The Regularized Visible Fold Revisited	15
Optimal Harvesting of Stochastic Population Models with Periodic Coefficients	15
A Geometric Heat-Flow Theory of Lagrangian Coherent Structures	15
2D Euler Equations with Stratonovich Transport Noise as a Large-Scale Stochastic Model Reduction	15
Propagation Speed of the Bistable Traveling Wave to the Lotka–Volterra Competition System in a Periodic Habitat	14
The Finite-Time Blow-Up for Semilinear Fractional Diffusion Equations with Time $$\psi $$-Caputo Derivative	14
Vortex Patches Choreography for Active Scalar Equations	13
Stochastic SIR Lévy Jump Model with Heavy-Tailed Increments	13

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

Finite-Dimensionality of Tempered Random Uniform Attractors	6
An Intrinsic Aggregation Model on the Special Orthogonal Group SO(3): Well-posedness and Collective Behaviours	6
Spike-Adding Canard Explosion in a Class of Square-Wave Bursters	6
Adaptive Dynamics of a Stoichiometric Phosphorus–Algae–Zooplankton Model with Environmental Fluctuations	6
Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in $${\mathbb {R}}^n$$: (I) Under-Damping Case	6
On the Motion of Gravity–Capillary Waves with Odd Viscosity	6
Stability Against the Odds: The Case of Chromonic Liquid Crystals	6
Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries	5
Closed 1/2-Elasticae in the 2-Sphere	5
Spontaneous Periodic Orbits in the Navier–Stokes Flow	5
Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory	5
Scaling Limits for the Generalized Langevin Equation	5
Localised Radial Patterns on the Free Surface of a Ferrofluid	5
Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy	5
Vortex Pairs and Dipoles on Closed Surfaces	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
Dynamics of a Stochastic SVEIR Epidemic Model Incorporating General Incidence Rate and Ornstein–Uhlenbeck Process	4
Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems: A New Approach Using Secants	4
The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation	4
Pushed-to-Pulled Front Transitions: Continuation, Speed Scalings, and Hidden Monotonicty	4
Analysis and Optimal Velocity Control of a Stochastic Convective Cahn–Hilliard Equation	4
Nilpotent Singularities and Periodic Perturbation of a $$GI\beta $$ Model: A Pathway to Glucose Disorder	4
Relaxation to Fractional Porous Medium Equation from Euler–Riesz System	4
Well-Posedness of Solutions for the Sixth-Order Boussinesq Equation with Linear Strong Damping and Nonlinear Source	4
Closed Unstretchable Knotless Ribbons and the Wunderlich Functional	4
Remarks on Liouville-Type Theorems for the Steady MHD and Hall-MHD Equations	4
Nonlinear Physiologically Structured Population Models with Two Internal Variables	4
Algae–Bacteria Interactions with Nutrients and Light: A Reaction–Diffusion–Advection Model	4
Analysis of a Stochastic HBV Infection Model with DNA-Containing Capsids and Virions	4
Modulation Theory for Radially Symmetric Kink Waves Governed by a Multi-Dimensional Sine-Gordon Equation	4
Two-Parameter Generalizations of Cauchy Bi-Orthogonal Polynomials and Integrable Lattices	4
Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions	4
Global Bifurcation of Anti-plane Shear Fronts	4
Synchronization Conditions of a Mixed Kuramoto Ensemble in Attractive and Repulsive Couplings	4
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 Linear Response for Markov Hilbert–Schmidt Integral Operators and Stochastic Dynamical Systems	4
Steady-State Bifurcation of a Non-parallel Flow Involving Energy Dissipation over a Hartmann Boundary Layer	4
Analysis of Group of Fish Response to Startle Reaction	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
Dynamics of Shadow System of a Singular Gierer–Meinhardt System on an Evolving Domain	4
A Multiscale Problem for Viscous Heat-Conducting Fluids in Fast Rotation	4
Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl	4