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Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 07/2019, Volume 74, pp. 84 - 96
In this paper, we consider the bifurcation of small amplitude isolated periodic wave trains (SAIPWT) and the monotonicity of wave length of the periodic wave... 
Periodic wave trains | Reaction-diffusion equation | Critical wave length | Critical period | Singular point value | EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | BIFURCATIONS | PHYSICS, FLUIDS & PLASMAS | MONOTONICITY | MODEL | PHYSICS, MATHEMATICAL | TRAVELING-WAVE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | LIMIT-CYCLES | WEAK CENTERS | Algebra
Journal Article
Astrophysical Journal, ISSN 0004-637X, 02/2017, Volume 836, Issue 1, p. 1
The behavior of the axial group speeds of trapped sausage modes plays an important role in determining impulsively generated wave trains, which have often been... 
Sun: flares | waves | Sun: corona | magnetohydrodynamics (MHD) | Sun: magnetic fields | MAGNETIC-FLUX TUBES | HIGH-FREQUENCY OSCILLATIONS | FLARE LOOPS | MAGNETOACOUSTIC WAVE | TIME SIGNATURES | MHD WAVES | ASTRONOMY & ASTROPHYSICS | NUMERICAL SIMULATIONS | QUASI-PERIODIC PULSATIONS | SOLAR RADIO-EMISSION | PROPAGATION | Physics - Solar and Stellar Astrophysics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2018, Volume 265, Issue 10, pp. 5315 - 5351
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2019, Volume 372, Issue 5, pp. 3487 - 3537
This work is mainly motivated by the study of periodic wave train solutions for the so-called Gurtin-McCamy equation. To that aim we construct a smooth center... 
integrated semigroups | PERIODIC-SOLUTIONS | Center manifold | periodic wave trains | THEOREM | second order semilinear equations | INVARIANT-MANIFOLDS | ANALYTIC SEMIGROUPS | TRAVELING-WAVES | MATHEMATICS | MODELS | DIFFUSION | ELLIPTIC-EQUATIONS | Hopf bifurcation | Gurtin-McCamy equation | AGE | Analysis of PDEs | Mathematics
Journal Article
Physics of Fluids, ISSN 1070-6631, 11/2016, Volume 28, Issue 11, p. 113604
We prove that in a regular wave train, which propagates at the surface of water in irrotational flow over a flat bed, the maximum and minimum of the dynamic... 
RECOVERY | VELOCITY | PROFILES | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PERIODIC WATER-WAVES | LARGE-AMPLITUDE | STOKES WAVES | TRAJECTORIES | CONSTANT VORTICITY | SURFACE GRAVITY-WAVES | BENEATH | Potential flow | Wave packets | Dynamic pressure
Journal Article
Nonlinearity, ISSN 0951-7715, 11/2018, Volume 31, Issue 12, pp. 5536 - 5572
We study invasion fronts in the FitzHugh-Nagumo equation in the oscillatory regime using singular perturbation techniques. Phenomenologically, localized... 
invasion fronts | geometric singular perturbation theory | spreading speed | FitzHugh-Nagumo | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | SINGULAR PERTURBATION-THEORY | STABILITY | PHYSICS, MATHEMATICAL | OSCILLATORY TAILS | PULSES | PERIODIC-ORBITS | MEDIA | DIFFUSION | PROPAGATION
Journal Article
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), ISSN 0272-4960, 05/2014, Volume 80, Issue 4, pp. 1155 - 1177
Journal Article
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, 01/2007, Volume 17, Issue 8, pp. 2679 - 2691
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2014, Volume 417, Issue 1, pp. 376 - 393
A diffusive predator–prey system with Ivlev-type scheme is investigated in this article. The existences of a small amplitude periodic traveling wave train and... 
Diffusive predator–prey system | Geometric singular perturbation | Periodic traveling wave train | Point-to-periodic traveling wave | Shooting method | Diffusive predator-prey system | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | LOTKA-VOLTERRA EQUATIONS | MODEL | TIME-DELAY
Journal Article
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), ISSN 0272-4960, 06/2013, Volume 78, Issue 3, pp. 513 - 536
The two-variable Oregonator model for the Belousov-Zhabotinsky reaction is considered over the parameter range when regular wave trains arise at large times.... 
Belousov-Zhabotinsky reaction | Oregonator model | matched asymptotic expansions | periodic wave trains | EXCITABLE MEDIA | MATHEMATICS, APPLIED | CHEMICAL-SYSTEMS | DISPERSION | OSCILLATIONS | BELOUSOV-ZHABOTINSKII REACTION | TRAVELING-WAVES | Asymptotic expansions | Evolution | Mathematical models | Numerical integration | Reaction kinetics | Wave packets
Journal Article
Nonlinearity, ISSN 0951-7715, 02/2009, Volume 22, Issue 2, pp. 283 - 299
We study the existence and branching patterns of wave trains in the one-dimensional infinite Fermi-Pasta-Ulam (FPU) lattice. A wave train Ansatz in this... 
PASTA-ULAM LATTICE | MATHEMATICS, APPLIED | MODES | VIBRATIONS | PERIODIC TRAVELING WAVES | CHAINS | PHYSICS, MATHEMATICAL
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2010, Volume 239, Issue 17, pp. 1670 - 1680
Journal Article
Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 12/2006, Volume 8, Issue 4, pp. 482 - 509
Journal Article
SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, 01/2006, Volume 5, Issue 4, pp. 634 - 649
We analyze geometric relations of absolute and essential spectra for certain linear operators on the real line with periodic coefficients. These spectra... 
wave trains | essential spectrum | MATHEMATICS, APPLIED | isolated spectral sets | STABILITY | absolute spectrum | reaction diffusion systems | PERIODIC TRAVELING WAVES | PHYSICS, MATHEMATICAL
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 1, pp. 477 - 497
We study periodic traveling waves (wave trains) in diatomic Fermi-Pasta-Ulam chains (FPU). By applying the minimax principle, we demonstrate the existence of... 
Minimax methods | Diatomic FPU chain | Wave trains | wave trains | minimax methods | FPU LATTICES | EXISTENCE | MATHEMATICS, APPLIED | diatomic FPU chain | DISCRETE PERIODIC MEDIUM | SOLITONS | SOLITARY WAVES | SYSTEMS | CHAINS | TRAVELING-WAVES | Functions (mathematics) | Trains | Wave propagation | Asymptotic properties | Mathematical analysis | Lattices | Waveforms | Wavenumber
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 11/2019, Volume 481, pp. 151 - 161
Landscape-scale vegetation stripes (tiger bush) observed on the gentle slopes of semi-arid regions are useful indicators of future ecosystem degradation and... 
Non-local | Self-organisation | Periodic travelling wave | Banded vegetation | Reaction-diffusion-advection | Desertification | Seed dispersal | Tiger bush | Resilience | WAVE-TRAINS | KLAUSMEIER MODEL | COLONIZATION | ORGANIZATION | AFRICA | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | SOIL | CONTINUATION | Seeds | Deserts | Ecosystems | Rain and rainfall | Analysis
Journal Article
Journal of Colloid and Interface Science, ISSN 0021-9797, 04/1997, Volume 188, Issue 1, pp. 16 - 26
We show how periodic wave trains are generated in liquid layers when the liquid is heated from above or when a surface-active vapor is absorbed at a liquid of... 
nonlinear wave interactions | oscillatory convection | traveling periodic wave trains | resonance | Marangoni effect | dissipative solitons | interfacial instability | Nonlinear wave interactions | Traveling periodic wave strains | Dissipative solitons | Resonance | Interfacial instability | Oscillatory convection
Journal Article
JOURNAL OF COLLOID AND INTERFACE SCIENCE, ISSN 0021-9797, 04/1997, Volume 188, Issue 1, pp. 16 - 26
We show how periodic wave trains are generated in liquid layers when the liquid is heated from above or when a surface-active vapor is absorbed at a liquid of... 
SOLITARY WAVES | nonlinear wave interactions | SURFACE | CHEMISTRY, PHYSICAL | oscillatory convection | BENARD CONVECTION | K EI CHEMISTRY, PHYSICAL | traveling periodic wave trains | resonance | Marangoni effect | dissipative solitons | interfacial instability
Journal Article