Studies in Applied Mathematics

Article	Citations
Completely resonant collision of lumps and line solitons in the Kadomtsev–Petviashvili I equation	65
Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies	53
Riemann–Hilbert problem and interactions of solitons in the ‐component nonlinear Schrödinger equations	40
Lump chains in the KP‐I equation	40
Spatiotemporal dynamics of a diffusive consumer‐resource model with explicit spatial memory	29
Bifurcation analysis of an extended Klausmeier–Gray–Scott model with infiltration delay	29
General soliton and (semi‐)rational solutions to the nonlocal Mel'nikov equation on the periodic background	25
Exotic wave patterns in Riemann problem of the high‐order Jaulent–Miodek equation: Whitham modulation theory	25
The Fokas–Lenells equations: Bilinear approach	23
Spatiotemporal patterns in a diffusive predator–prey system with nonlocal intraspecific prey competition	21
The regularity of the multiple higher‐order poles solitons of the NLS equation	21
Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system	20
Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales	20
Darboux transformations and solutions of nonlocal Hirota and Maxwell–Bloch equations	18
Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction	17
General soliton solutions to a reverse‐time nonlocal nonlinear Schrödinger equation	16
Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators	16
Linking bifurcation analysis of Holling–Tanner model with generalist predator to a changing environment	16
Integrability, existence of global solutions, and wave breaking criteria for a generalization of the Camassa–Holm equation	15
The short pulse equation: Bäcklund transformations and applications	14
Improved finite‐time zeroing neural network for time‐varying division	14
High‐order exceptional points and enhanced sensing in subwavelength resonator arrays	14
New finite volume approach for multidimensional Smoluchowski equation on nonuniform grids	13
Long‐time asymptotic behavior of the fifth‐order modified KdV equation in low regularity spaces	13
Optimal quarantine‐related strategies for COVID‐19 control models	13

Dynamics of the predator–prey model with the Sigmoid functional response	12
Dispersive Riemann problems for the Benjamin–Bona–Mahony equation	11
Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants	11
Real Lax spectrum implies spectral stability	11
Exact solutions and internal waves for the Antarctic Circumpolar Current in spherical coordinates	10
Inverse scattering transform for the complex coupled short‐pulse equation	10
Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows	10
Stability of smooth periodic travelling waves in the Camassa–Holm equation	10
Local symmetry structure and potential symmetries of time‐fractional partial differential equations	9
Kernel density estimation with linked boundary conditions	9
Sparse spectral and ‐finite element methods for partial differential equations on disk slices and trapeziums	9
Existence, uniqueness and stability of forced waves to the Lotka‐Volterra competition system in a shifting environment	9
Infinite time blow‐up of solutions to a class of wave equations with weak and strong damping terms and logarithmic nonlinearity	9
Analyticity of rotational traveling gravity two‐layer waves	9
Dispersive shock waves for the Boussinesq Benjamin–Ono equation	8
Molecular dynamics simulations to explore the structure and rheological properties of normal and hyperconcentrated airway mucus	8
Dissipative models of swell propagation across the Pacific	8
Stability in distribution for age‐structured HIV model with delay and driven by Ornstein–Uhlenbeck process	8
Vector breathers in the Manakov system	8
The complex Hamiltonian systems and quasi‐periodic solutions in the derivative nonlinear Schrödinger equations	8
Riemann–Hilbert approach for discrete sine‐Gordon equation with simple and double poles	8
Numerical study of the transverse stability of the Peregrine solution	8
Sharp estimate of electric field from a conductive rod and application	8
On the existence and regularity of solutions of semihyperbolic patches to 2‐D Euler equations with van der Waals gas	8
Consensus‐based sampling	7
Properties of given and detected unbounded solutions to a class of chemotaxis models	7
Cauchy matrix approach to the SU(2) self‐dual Yang–Mills equation	7
Spot patterns in the 2‐D Schnakenberg model with localized heterogeneities	7
General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model	7
Bifurcations of thresholds in essential spectra of elliptic operators under localized non‐Hermitian perturbations	6
Spatial propagation in a within‐host viral infection model	6
Invasion analysis of a two‐species Lotka–Volterra competition model in an advective patchy environment	6
Doubly periodic lozenge tilings of a hexagon and matrix valued orthogonal polynomials	6
Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line	6
Analytical construction of soliton families in one‐ and two‐dimensional nonlinear Schrödinger equations with nonparity‐time‐symmetric complex potentials	6
Mass‐in‐mass lattices with small internal resonators	6
Multiple orthogonal polynomials with respect to Gauss' hypergeometric function	6
On the almost‐circular symplectic induced Ginibre ensemble	6
Electromagnetic interactions of dipole distributions with a stratified medium: Power fluxes and scattering cross sections	6
A novel fractional‐order reaction diffusion system for the multiplicative noise removal	6
On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation	6
Tau‐function formulation for bright, dark soliton and breather solutions to the massive Thirring model	5
Quasi‐stability and upper semicontinuity for coupled parabolic equations with memory	5
The linearized classical Boussinesq system on the half‐line	5
Hölder stability and uniqueness for the mean field games system via Carleman estimates	5
Superharmonic instability of stokes waves	5
Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations	5
Stable blow‐up dynamics in the ‐critical and ‐supercritical generalized Hartree equation	5
Measures to assess a warning vaccination level in a stochastic SIV model with imperfect vaccine	5
Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systems	5

On an averaged model for immiscible two‐phase flow with surface tension and dynamic contact angle in a thin strip	5
Uniform error estimates for the random batch method to the first‐order consensus models with antisymmetric interaction kernels	5
New revival phenomena for linear integro–differential equations	5
Traveling capillary waves on the boundary of a fluid disc	5
Multiscale expansions avector solitons of a two‐dimensional nonlocal nonlinear Schrödinger system	5
Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies	5
Squared eigenfunction symmetry of the DmKP hierarchy and its constraint	5
Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation	5
Capillary‐gravity solitary waves on water of finite depth interacting with a linear shear current	4
An invariant for colored bonded knots	4
The unified transform for evolution equations on the half‐line with time‐periodic boundary conditions*	4
A simplified monotone model of Wolbachia invasion encompassing Aedes aegypti mosquitoes	4
Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid	4
Whitham modulation theory for generalized Whitham equations and a general criterion for modulational instability	4
Zeroth‐order conservation laws of two‐dimensional shallow water equations with variable bottom topography	4
Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary	4
Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies	4
Scattering and inverse scattering for the AKNS system: A rational function approach	4
Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation	4
Connection formulae for asymptotics of the fifth Painlevé transcendent on the imaginary axis: I	4
Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics	4
Curved wedges in the long‐time asymptotics for the integrable nonlocal nonlinear Schrödinger equation	4
Dependence of eigenvalues of Dirac system on the parameters	4
On the Whitham system for the (2+1)‐dimensional nonlinear Schrödinger equation	4
The 2D magnetohydrodynamic system with Euler‐like velocity equation and partial magnetic diffusion	4
Dynamical analysis of an age‐structured SIRE epidemic model with two routes of infection in environment	4
The binary Darboux transformation revisited and KdV solitons on arbitrary short‐range backgrounds	4
Solitary waves in a Whitham equation with small surface tension	4
Semiclassical dynamics and coherent soliton condensates in self‐focusing nonlinear media with periodic initial conditions	4
Exact analytical solution of a novel modified nonlinear Schrödinger equation: Solitary quantum waves on a lattice	4
A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions	4
Canonical conformal variables based method for stability of Stokes waves	3
Periodic problem for the nonlinear damped wave equation with convective nonlinearity	3
On the three‐dimensional consistency of Hirota's discrete Korteweg‐de Vries equation	3
Wave–current interaction on a free surface	3
Distance distributions and inverse problems for metric measure spaces	3
On nonexistence of continuous families of stationary nonlinear modes for a class of complex potentials	3
Rigorous justification of the Whitham modulation theory for equations of NLS type	3
Spatiotemporal dynamics in a twisted, circular waveguide array	3
The evolution of traveling waves in a KPP reaction‐diffusion model with cut‐off reaction rate. I. Permanent form traveling waves	3
Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials	3
Energy thresholds of blow‐up for the Hartree equation with a focusing subcritical perturbation	3
A Novikov equation describing pseudo‐spherical surfaces, its pseudo‐potentials, and local isometric immersions	3
Ocean‐depth measurement using shallow‐water wave models	3
Asymptotic solutions of inhomogeneous differential equations having a turning point	3
Radiation of waves by a submerged nearly circular rough plate in ice‐covered ocean	3
Rogue waves in the massive Thirring model	3
Essential spectra of singular Hamiltonian differential operators of arbitrary order under a class of perturbations	3
Ladder relations for a class of matrix valued orthogonal polynomials	3
On the stochastic robustness of complete clustering predictability for a first‐order consensus model	3
The multi elliptic‐localized solutions and their asymptotic behaviors for the mKdV equation	3
Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems	3
On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation	3
Kinetic energy of the Langevin particle	3
Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability	3
Direct and inverse scattering problems for the first‐order discrete system associated with the derivative NLS system	3
Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates	3
The numerical solutions of linear semidiscrete evolution problems on the half‐line using the Unified Transform Method	3
Breather solutions for a quasi‐linear ‐dimensional wave equation	3
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Asymptotic behavior of the porous elastic system with dual phase lag model: Classical versus second spectrum perspectives	2
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Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel	2
Traveling waves, blow‐up, and extinction in the Fisher–Stefan model	2
Stability of 3D perturbations near a special 2D solution to the rotating Boussinesq equations	2
The classical Neumann problem for a class of mixed Hessian equations	2
Partial differential equations admitting a given nonclassical point symmetry	2
Near‐optimal control of a stochastic model for mountain pine beetles with pesticide application	2
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Linear integral equations and two‐dimensional Toda systems	2
Global‐phase portrait and large‐degree asymptotics for the Kissing polynomials	2
Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations	2
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Solutions to a phase‐field model for martensitic phase transformations driven by configurational forces	2
Uniform (very) sharp bounds for ratios of parabolic cylinder functions	2
An SIS epidemic model with mass action infection mechanism in a patchy environment	2
Higher dimensional generalization of the Benjamin‐Ono equation: 2D case	2
Dynamics of a nonlocal dispersal in‐host viral model with humoral immunity	2
Integrability and solvability of polynomial Liénard differential systems	2

The elliptical vortices, integrable Ermakov structure, Schrödinger connection, and Lax pair in the compressible Navier–Stokes equation	2
Rogue wave patterns associated with Okamoto polynomial hierarchies	2
Polynomial ergodicity of an SIRS epidemic model with density‐dependent demographics	2
Convergence rates of vanishing diffusion limit on conservative form of Hsieh's equation	2
Well‐posedness of solutions for a class of quasilinear wave equations with strong damping and logarithmic nonlinearity	2
The evolution of traveling waves in a KPP reaction–diffusion model with cut‐off reaction rate. II. Evolution of traveling waves	2
Exceptional Gegenbauer polynomials via isospectral deformation	2
Systematic construction of nonautonomous Hamiltonian equations of Painlevé‐type. II. Isomonodromic Lax representation	2
Well‐posedness and control in a hyperbolic–parabolic parasitoid–parasite system	2
Traveling wave solutions in a model for social outbursts in a tension‐inhibitive regime	2
On analyticity of scattered fields in layered structures with interfacial graphene	2
Soliton interactions and Yang–Baxter maps for the complex coupled short‐pulse equation	2
Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method	2
Stäckel transform of Lax equations	2
Dynamics for a quantum parliament	2
Transmission properties of space‐time modulated metamaterials	2
Impact of nonlocal dispersal and time periodicity on the global exponential stability of bistable traveling waves	2
Singular Sturm–Liouville operators with extreme properties that generate black holes	2
Nonlinearizable solutions in an eigenvalue problem for Maxwell's equations with nonhomogeneous nonlinear permittivity in a layer	2
Isentropic approximation of the compressible Euler equations in Besov spaces	1
A note about the invariance of the basic reproduction number for stochastically perturbed SIS models	1
Stability of the inverse scattering problem for the self‐adjoint matrix Schrödinger operator on the half line	1
Differential equations for the recurrence coefficients of semiclassical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach	1
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Green's functions, linear second‐order differential equations, and one‐dimensional diffusion advection models	1
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Initial boundary value problem for a class of wave equations of Hartree type	1
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Nonuniform laminated beam of Lord–Shulman type	1
Self‐contained two‐layer shallow‐water theory of strong internal bores	1
Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters	1
On the variation of bi‐periodic waves in the transverse direction	1
Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl	1
Rigorous justification of the Whitham modulation equations for equations of Whitham type	1
Exploring the interplay between memory effects and vesicle dynamics: A five‐dimensional analysis using rigid sphere models and mapping techniques	1
Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation	1
Subharmonic dynamics of wave trains in the Korteweg‐de Vries/Kuramoto‐Sivashinsky equation	1
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Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples	1
From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems	1
Linearizable Abel equations and the Gurevich–Pitaevskii problem	1
An integrable semidiscretization of the modified Camassa–Holm equation with linear dispersion term	1
On ground states for the 2D Schrödinger equation with combined nonlinearities and harmonic potential	1
On the Su–Schrieffer–Heeger model of electron transport: Low‐temperature optical conductivity by the Mellin transform	1
Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation	1
Two‐dimensional Riemann problem of the Euler equations to the Van der Waals gas around a sharp corner	1
Using Symmetries à Rebours	1
Spatial dynamics for an SIRE epidemic model with diffusion and prevention in contaminated environments	1
Multidimensional conservation laws and integrable systems II	1
Viscosity solutions to a Cauchy problem of a phase‐field model for solid‐solid phase transitions	1
Large‐time asymptotics to the focusing nonlocal modified Kortweg‐de Vries equation with step‐like boundary conditions	1
Higher‐order symmetries of underdetermined systems of partial differential equations and Noether's Second Theorem	1
Local well‐posedness of the higher‐order nonlinear Schrödinger equation on the half‐line: Single‐boundary condition case	1
Resurgent aspects of applied exponential asymptotics	1
New and simple mathematical description of epidemics including consecutive waves	1
Epidemic dynamics and spatial segregation driven by cognitive diffusion and nonlinear incidence	1
Macroscopic wave propagation for 2D lattice with random masses	1
Orthogonal polynomials on a class of planar algebraic curves	1
Landscape of wave focusing and localization at low frequencies	1
Traveling waves in a coarse‐grained model of volume‐filling cell invasion: Simulations and comparisons	1
Isomonodromy sets of accessory parameters for Heun class equations	1
On mixed problem of Chaplygin's hodograph equation in hyperbolic domain near the parabolic degenerate line	1
On the linearized system of equations for the condensate–normal fluid interaction at very low temperature	1
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On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve	1
The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics	1
Dynamics of the rogue lump in the asymmetric Nizhnik–Novikov–Veselov system	1
Asymptotics of solutions to periodic problem for the Korteweg–de Vries–Burgers equation	1
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Radial spiky steady states of a flux‐limited Keller–Segel model: Existence, asymptotics, and stability	1
Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations	1
Numerical study of Davey–Stewartson I systems	1
Oscillations in three‐reaction quadratic mass‐action systems	1
Language competition on lattices	1
A Markov chain model to investigate the spread of antibiotic‐resistant bacteria in hospitals	1