Physica D-Nonlinear Phenomena

Article	Citations
Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network	1837
Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales	138
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems	130
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control	125
Accurate closed-form solution of the SIR epidemic model	78
Time-series learning of latent-space dynamics for reduced-order model closure	68
Inversion of a SIR-based model: A critical analysis about the application to COVID-19 epidemic	68
Riemann–Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies	64
COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility	59
Periodic standing waves in the focusing nonlinear Schrödinger equation: Rogue waves and modulation instability	45
Predicting the evolution of the COVID-19 epidemic with the A-SIR model: Lombardy, Italy and São Paulo state, Brazil	45
Explicit formulae for the peak time of an epidemic from the SIR model	44
Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows	42
Rogue wave patterns in the nonlinear Schrödinger equation	41
Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation	40
A long short-term memory embedding for hybrid uplifted reduced order models	38
Riemann–Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions	35
Bistability, wave pinning and localisation in natural reaction–diffusion systems	35
Size and timescale of epidemics in the SIR framework	35
N-double poles solutions for nonlocal Hirota equation with nonzero b	35
On the emergence of a power law in the distribution of COVID-19 cases	35
Analytic solution of the SEIR epidemic model via asymptotic approximant	34
Sasa–Satsuma type matrix integrable hierarchies and their Riemann–Hilbert problems and soliton solutions	34
Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning	32
A Reduced Order Deep Data Assimilation model	32

Data-driven predictions of the Lorenz system	31
A data-driven approach for discovering stochastic dynamical systems with non-Gaussian Lévy noise	31
Higher-order rogue wave solutions to the Kadomtsev–Petviashvili 1 equation	31
The Shannon entropy: An efficient indicator of dynamical stability	29
Association between COVID-19 cases and international equity indices	29
A simple but complex enough θ-SIR type model to be used with COVID-1	29
Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits	29
Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada–Kotera equation	28
Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions	27
Evolutionary dynamics of cooperation in the N-person stag hunt game	27
Operator-theoretic framework for forecasting nonlinear time series with kernel analog techniques	27
Universal rogue wave patterns associated with the Yablonskii–Vorob’ev polynomial hierarchy	27
Darboux transformation and solitonic solution to the coupled complex short pulse equation	27
Echo State Networks trained by Tikhonov least squares are L	26
Exotic vector freak waves in the nonlocal nonlinear Schrödinger equation	26
The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer–Meshkov instability	25
Kadomtsev–Petviashvili equation: One-constraint method and lump pattern	25
Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning	24
Trends in COVID-19 prevalence and mortality: A year in review	24
Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil	23
Nested mixed-mode oscillations, part II: Experimental and numerical study of a classical Bonhoeffer–van der Pol oscillator	23
Novel semi-metrics for multivariate change point analysis and anomaly detection	22
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity	22
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation	22
Higher-order algebraic soliton solutions of the Gerdjikov–Ivanov equation: Asymptotic analysis and emergence of rogue waves	21
Mechanisms of stationary converted waves and their complexes in the multi-component AB system	21
Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions	21
Riemann–Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions	21
Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems	20
New approximations, and policy implications, from a delayed dynamic model of a fast pandemic	20
Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation	20
Hamiltonian structure of compartmental epidemiological models	20
Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?	19
Multi-lump solutions of KP equation with integrable boundary via	19
Variable-density buoyancy-driven turbulence with asymmetric initial density distribution	19
A sharp-front moving boundary model for malignant invasion	18
Birkhoff averages and rotational invariant circles for area-preserving maps	18
Non-degenerate multi-rogue waves and easy ways of their excitation	18
Semi-rational vector rogon–soliton solutions and asymptotic analysis for anyn	18
A vector Geng–Li model: New nonlinear phenomena and breathers on periodic background waves	18
A look into chaos detection through topological data analysis	18
Effects of precipitation intermittency on vegetation patterns in semi-arid landscapes	17
Rayleigh–Taylor instability with gravity reversal	17
Resonant collision of lumps with homoclinic orbits in the two-dimensional multi-component long-wave–short-wave resonance interaction systems	17
Planning of school teaching during Covid-19	17
Modeling cell crawling strategies with a bistable model: From amoeboid to fan-shaped cell motion	17
Kernel-based prediction of non-Markovian time series	16
The robust inverse scattering method for focusing Ablowitz–Ladik equation on the non-vanishing background	16
Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol–Duffing and the Rayleigh–Duffing oscillators	16
Expectation-maximizing network reconstruction and most applicable network types based on binary time series data	15

The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation	15
Poincaré maps for multiscale physics discovery and nonlinear Floquet theory	15
Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method	15
Asymptotic analysis of high-order solitons for the Hirota equation	15
Memory and forecasting capacities of nonlinear recurrent networks	14
A novel antimonotic hyperjerk system: Analysis, synchronization and circuit design	13
Data-driven rogue waves and parameters discovery in nearly integrable	13
Rogue waves in (2+1)-dimensional three-wave resonant interactions	13
Statistical basin of attraction in time-delayed cutting dynamics: Modelling and computation	13
Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system	13
Towards the Heider balance with a cellular automaton	13
Breathers, cascading instabilities and Fermi–Pasta–Ulam–Tsingou recurrence of the derivative nonlinear Schrödinger equation: Effects of ‘self-steepening’ nonlinearity	13
Dissecting the snake: Transition from localized patterns to spike solutions	13
Conservative, dissipative and super-diffusive behavior of a particle propelled in a regular flow	13
Pattern formation in hyperbolic models with cross-diffusion: Theory and applications	13
Vortex morphology in Richtmyer–Meshkov-induced turbulent mixing	12
A fast–slow model of banded vegetation pattern formation in drylands	12
On Hamiltonian continuum mechanics	12
On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto–Sivashinsky equation	12
Beyond rock–paper–scissors systems — Deterministic models of cyclic ecological systems with more than three species	12
Enhanced energy harvesting using time-delayed feedback control from random rotational environment	12
Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer–van der Pol oscillator	12
Explosive, continuous and frustrated synchronization transition in spiking Hodgkin–Huxley neural networks: The role of topology and synaptic interaction	11
Solutions to the Kaup–Broer system and its (2＋1) dimensional integrable generalization via the dressing method	11
A subdiffusive Navier–Stokes–Voigt system	11
Data-driven discovery of emergent behaviors in collective dynamics	11
Bayesian learning of stochastic dynamical models	11
Supervised learning algorithms for controlling underactuated dynamical systems	11
On the double sphere model of synchronization	11
Pressure effect on the formation kinetics of ferroelectric domain structure under first order phase transitions	11
Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES	11
Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization	11
Shape of pendent droplets under a tilted surface	11
Emergent behaviors of relativistic flocks on Riemannian manifolds	11
Higher-dimensional soliton generation, stability and excitations of the 11
Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems	11
Multi-component universal character hierarchy and its polynomial tau-functions	11
Opinion dynamics involving contrarian and independence behaviors based on the Sznajd model with two-two and three-one agent interactions	11
Control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning	10
The influence of autotoxicity on the dynamics of vegetation spots	10
Nonlinear feedback control of Marangoni wave patterns in a thin film heated from below	10
Large speed traveling waves for the Rosenzweig–MacArthur predator–prey model with spatial diffusion	10
Scaling effect in COVID-19 spreading: The role of heterogeneity in a hybrid ODE-network model with restrictions on the inter-cities flow	10
Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems	10
Coarse grained simulation of convectively driven turbulent mixing, transition, and turbulence decay	10
High speed PLIF study of the Richtmyer–Meshkov instability upon re-shock	10
On long-time asymptotics to the nonlocal short pulse equation with the Schwartz-type initial data: Without solitons	10
Neural networks enforcing physical symmetries in nonlinear dynamical lattices: The case example of the Ablowitz–Ladik model	10
Travelling wave analysis of cellular invasion into surrounding tissues	10
Understanding the transport and break up of reactive ejecta	10
Solution landscape of the Onsager model identifies non-axisymmetric critical points	10
Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers	10
Application of Lie point symmetries to the resolution of an interface problem in a generalized Fisher equation	10
General breather and rogue wave solutions to the complex short pulse equation	9
Higher-order optical rogue waves in spatially inhomogeneous multimode fiber	9
Kernel methods for center manifold approximation and a weak data-based version of the Center Manifold Theorem	9
The echo index and multistability in input-driven recurrent neural networks	9
Linearized fast time-stepping schemes for time–space fractional Schrödinger equations	9
Interactions of two bubbles along a gaseous interface undergoing the Richtmyer–Meshkov instability in two dimensions	9
Traveling pulses in a coupled FitzHugh–Nagumo equation	9
The αs and 9
Computing with non-orientable defects: Nematics, smectics and natural patterns	9
The generalized fractional Benjamin–Bona–Mahony equation: Analytical and numerical results	9
Estimating parameters of the nonlinear cloud and rain equation from a large-eddy simulation	9
Formation of the undular bores in shallow water generalized Kaup–Boussinesq model	9
Birkhoff averages and the breakdown of invariant tori in volume-preserving maps	9
Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression	9
Micropteron traveling waves in diatomic Fermi–Pasta–Ulam–Tsingou lattices under the equal mass limit	9
Solitary waves in FPU-type lattices	9
A general view on double limits in differential equations	9
Learning mean-field equations from particle data using WSINDy	9
The nature of reactive and non-reactive trajectories for a three dimensional Caldera potential energy surface	9
Interactions of fractional N-solitons with anomalous dispersions for	8
The structure of algebraic solitons and compactons in the generalized Korteweg–de Vries equation	8
Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators	8
Chiral skyrmions of large radius	8
Grassmannian flows and applications to non-commutative non-local and local integrable systems	8
Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin–Ono equation	8
Progress, gaps and obstacles in the classification of cellular automata	8
Evolutionary correlation, regime switching, spectral dynamics and optimal trading strategies for cryptocurrencies and equities	8

Dynamic transitions and bifurcations for thermal convection in the superposed free flow and porous media	8
Aspect-ratio-constrained Rayleigh–Taylor instability	8
The optimal decay rate of strong solution for the compressible Navier–Stokes equations with large initial data	8
Interaction between vegetation patches and gaps: A self-organized response to water scarcity	8
Shock-fronted travelling waves in a reaction–diffusion model with nonlinear forward–backward–forward diffusion	8
An overview on recent machine learning techniques for Port Hamiltonian systems	8
Mixed turbulence of breathers and narrowband irregular waves: mKdV framework	8
Adding filters to improve reservoir computer performance	8
Occurrence of Vibrational resonance in an oscillator with an asymmetric Toda potential	8
Dynamic coupling in small-world outer synchronization of chaotic networks	8
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler–Bardina equations	8
Algorithms of data generation for deep learning and feedback design: A survey	8
Topology of dynamical reconstructions from Lagrangian data	8
Buoyancy–Drag modelling of bubble and spike distances for single-shock Richtmyer–Meshkov mixing	8
PT-symm	8
Periodic waves in the discrete mKdV equation: Modulational instability and rogue waves	7
Long-time asymptotics for an integrable evolution equation with a 3 × 3 Lax pair	7
Radiation dynamics in fast soliton collisions in the presence of cubic loss	7
Deep regularization and direct training of the inner layers of Neural Networks with Kernel Flows	7
Switching between periodic orbits in impact oscillator by time-delayed feedback methods	7
Deep learning based classification of time series of Chen and Rössler chaotic systems over their graphic images	7
Bursting oscillations of the perturbed quasi-zero stiffness system with positive/negative stiffness at origin	7
Bilinear equations in Darboux transformations by Boson–Fermion correspondence	7
General rogue wave solutions under SU(2) transformation in the vector Chen–Lee–Liu nonlinear Schrödinger equation	7
Hidden Akhmediev breathers and vector modulation instability in the defocusing regime	7
Persistent strange attractors in 3D polymatrix replicators	7
Evolution of hybrid quantum–classical wavefunctions	7
Long time asymptotics for the nonlocal mKdV equation with finite density initial data	7
Snaking branches of planar BCC fronts in the 3D Brusselator	7
Control of diffusion-driven pattern formation behind a wave of competency	7
The Riemann problem for the one-dimensional isentropic Euler system under the body force with varying gamma law	7
Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media	7
Multi-soliton solutions of KP equation with integrable boundary via	7
Mathematical analysis of a Sips-based model for column adsorption	7
Two-dimensional patterns in dip coating - first steps on the continuation path	7
On vortex and dark solitons in the cubic–quintic nonlinear Schrödinger equation	7
VC-PINN: Variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient	7
Bridging the gap: Machine learning to resolve improperly modeled dynamics	7
Constants of motion for the finite-dimensional Lohe type models with frustration and applications to emergent dynamics	7
2D single-mode Richtmyer–Meshkov instability	7
Machine learning control — explainable and analyzable methods	6
Synchronization patterns on networks of pancreatic β-cell models	6
Hamiltonian chaos and differential geometry of configuration space–time	6
Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems	6
General rogue wave solution to the discrete nonlinear Schrödinger equation	6
A split-and-perturb decomposition of number-conserving cellular automata	6
Epidemic models with discrete state structures	6
Controlling coexisting attractors of a class of non-autonomous dynamical systems	6
Fast basin stability estimation for dynamic systems under large perturbations with sequential support vector machine	6
Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method	6
Pseudo-Hamiltonian neural networks with state-dependent external forces	6
Corrigendum and addendum to “Computation of domains of analyticity for the dissipative standard map in the limit of small dissipation” [Physica D 395 (2019) 15–23]	6
Complex dynamics on the one-dimensional quantum droplets via time piecewise PINNs	6
Darboux transformation and soliton solutions of the spatial discrete coupled complex short pulse equation	6
Equivalence relations and Lp	6
Rational vector rogue waves for the n-component Hirota equation wit	6
Wandering bumps in a stochastic neural field: A variational approach	6
Jensen–Fisher information and Jensen–Shannon entropy measures based on complementary discrete distributions with an application to Conway’s game of life	6
Local and nonlocal solitons in a coupled real system of Landau–Lifshitz equations	6
Global dynamics of hybrid van der Pol–Rayleigh oscillators	6
The stability of reacting single-mode Rayleigh–Taylor flames	6
High order rational solitons and their dynamics of the 3-wave resonant interaction equation	6
Crisis and hyperchaos in a simplified model of magnetoconvection	6
Basic reproduction number for the SIR epidemic in degree correlated networks	6
On first integrals and stability of stationary motions of gyrostat	6
On a class of new nonlocal traffic flow models with look-ahead rules	6
Deep learning soliton dynamics and complex potentials recognition for 1D and 2D	6
On the stability of traveling wave solutions to thin-film and long-wave models for film flows inside a tube	6
Stochastic deformations of coupling-induced oscillatory regimes in a system of two logistic maps	6
Deep learning of conjugate mappings	6
Flame propagation in a porous medium	6
Patterns, localized structures and fronts in a reduced model of clonal plant growth	6
Riemann–Hilbert approach and long-time asymptotics of the positive flow short-pulse equation	6
Wobbling kinks in a two-component scalar field theory: Interaction between shape modes	6
Interaction structures of multi localized waves within the Kadomtsev–Petviashvili I equation	5
The mathematics of burger flipping	5
Poisson–Nernst–Planck equations with high-order steric effects	5
Revisiting the relation between the Lyapunov time and the instability time	5
On the long time behavior of time relaxation model of fluids	5
A passive model for the evolution of subgrid-scale instabilities in turbulent flow regimes	5
Ginzburg–Landau model of a Stiffnessometer — A superconducting stiffness meter device	5
Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning	5
A view of the peakon world through the lens of approximation theory	5
Network of networks: A bibliometric analysis	5
Information quantity evaluation of nonlinear time series processes and applications	5
Orthogonal polynomials, Toda lattices and Painlevé equations	5
Discontinuity mappings for stochastic nonsmooth systems	5
Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model	5
Computation of large-genus solutions of the Korteweg–de Vries equation	5
Potential well escape via vortex-induced vibrations: A single-degree-of-freedom analysis	5
A crisis for the verification and validation of turbulence simulations	5
Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows	5
Sparse methods for automatic relevance determination	5
Rhombic and hexagonal pattern formation in 2D hyperbolic reaction–transport systems in the context of dryland ecology	5
Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary	5