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## Search Articles

Journal of the atmospheric sciences, ISSN 0022-4928, 04/2016, Volume 73, Issue 4, pp. 1755 - 1766

Very strong El Nino events occur sporadically every 10-20 yr. The origin of this bursting behavior still remains elusive. Using a simplified three-dimensional...

Atm/Ocean structure/ Phenomena | Nonlinear models | El Nino | ENSO | Southern oscillation | Circulation/ dynamics | Differential equations | Mathematical and statistical techniques | La Nina | Models and modeling | Meteorology & Atmospheric Sciences | Physical Sciences | Science & Technology

Atm/Ocean structure/ Phenomena | Nonlinear models | El Nino | ENSO | Southern oscillation | Circulation/ dynamics | Differential equations | Mathematical and statistical techniques | La Nina | Models and modeling | Meteorology & Atmospheric Sciences | Physical Sciences | Science & Technology

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2017, Volume 145, Issue 1, pp. 363 - 377

We study the spectrum of the Schrodinger operators with n x n matrix valued potentials on a finite interval subject to theta-periodic boundary conditions. For...

Eigenvalues | Hamiltonian systems | Differential operators | Stability | Discrete spectrum | Schrödinger equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Eigenvalues | Hamiltonian systems | Differential operators | Stability | Discrete spectrum | Schrödinger equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Physica. D, ISSN 0167-2789, 11/2016, Volume 334, pp. 4 - 18

We develop a stability index for the traveling waves of non-linear reaction–diffusion equations using the geometric phase induced on the Hopf bundle S2n−1⊂Cn....

Evans function | Traveling waves | Stability analysis | Geometric dynamics | Steady states | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology

Evans function | Traveling waves | Stability analysis | Geometric dynamics | Steady states | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology

Journal Article

Physica. D, ISSN 0167-2789, 05/2013, Volume 251, pp. 63 - 74

We study the spectral stability properties of periodic traveling waves in the sine–Gordon equation, including waves of both subluminal and superluminal...

Nonlinear waves | Periodic traveling waves | Stability | Partial differential equations | Sine–Gordon equation | Spectral analysis | Sine-Gordon equation | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology

Nonlinear waves | Periodic traveling waves | Stability | Partial differential equations | Sine–Gordon equation | Spectral analysis | Sine-Gordon equation | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology

Journal Article

2001, The IMA volumes in mathematics and its applications, ISBN 0387951261, Volume 122, xi, 263

Book

Boletim da Sociedade Brasileira de Matemática, ISSN 1678-7544, 6/2016, Volume 47, Issue 2, pp. 417 - 429

...) / 1678-7714 (Online)
On the Spectral and Modulational Stability
of Periodic W avetrains for Nonlinear
Klein-Gordon Equations
Christopher K.R.T. Jones, Robert Marangell...

37J25 | nonlinear Klein-Gordon equation | spectral stability | 35L70 | modulation theory | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | 70H12 | periodic wavetrains

37J25 | nonlinear Klein-Gordon equation | spectral stability | 35L70 | modulation theory | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | 70H12 | periodic wavetrains

Journal Article

Physica. D, ISSN 0167-2789, 12/2017, Volume 360, pp. 36 - 45

We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent...

Lagrangian data | Coherent structures | Data assimilation | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology | Tracers (Biology) | Analysis | Physics - Atmospheric and Oceanic Physics

Lagrangian data | Coherent structures | Data assimilation | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology | Tracers (Biology) | Analysis | Physics - Atmospheric and Oceanic Physics

Journal Article

Discrete and continuous dynamical systems, ISSN 1078-0947, 02/2017, Volume 37, Issue 2, pp. 859 - 878

Algae in the ocean absorb carbon dioxide from the atmosphere and thus play an important role in the carbon cycle. An algal bloom occurs when there is a rapid...

Phytoplankton | Non-local | Reaction-diffusion-advection | Phase space | Existence and uniqueness | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Phytoplankton | Non-local | Reaction-diffusion-advection | Phase space | Existence and uniqueness | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

SIAM journal on applied dynamical systems, ISSN 1536-0040, 01/2018, Volume 17, Issue 1, pp. 754 - 787

The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as...

Stability | Traveling waves | Geometric singular perturbation theory | FitzHugh–Nagumo | Transversality | Maslov index | Non–self-adjoint | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Stability | Traveling waves | Geometric singular perturbation theory | FitzHugh–Nagumo | Transversality | Maslov index | Non–self-adjoint | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Journal Article

SIAM journal on applied dynamical systems, ISSN 1536-0040, 2008, Volume 7, Issue 4, pp. 1558 - 1581

...SIAM J. APPLIED DYNAMICAL SYSTEMS c Vol. 7, No. 4, pp. 15581581 Electrical Waves in a One-Dimensional Model of Cardiac Tissue Margaret Beck, Christopher K. R...

Evans function | Cardiac model | Geometric singular perturbation theory | Alternans | Arrhythmia | Blow-up | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Evans function | Cardiac model | Geometric singular perturbation theory | Alternans | Arrhythmia | Blow-up | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology

Journal Article

Journal of dynamics and differential equations, ISSN 1040-7294, 12/2009, Volume 21, Issue 4, pp. 607 - 622

The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed...

Ordinary Differential Equations | Multi-pulses | Singular perturbation | Short pulse | Mathematics | Orbit flip | Lin’s method | Applications of Mathematics | Partial Differential Equations | Lin's method | Physical Sciences | Mathematics, Applied | Science & Technology | Physics - Pattern Formation and Solitons

Ordinary Differential Equations | Multi-pulses | Singular perturbation | Short pulse | Mathematics | Orbit flip | Lin’s method | Applications of Mathematics | Partial Differential Equations | Lin's method | Physical Sciences | Mathematics, Applied | Science & Technology | Physics - Pattern Formation and Solitons

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 1, pp. 517 - 548

... Paul Cornwell and Christopher K. R. T. Jones Department of Mathematics, UNC Chapel Hill, Phillips Hall CB #3250, Chapel Hill, NC 2 7516, USA (pcorn@live.unc.edu...

topological indices | solitary waves | homoclinic orbits | Evans function | non-self-adjoint eigenvalue problems | Maslov index | stability of travelling waves | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Stability | Inhibitors | Planes | Eigenvalues | Traveling waves | Conjugate points | Eigen values

topological indices | solitary waves | homoclinic orbits | Evans function | non-self-adjoint eigenvalue problems | Maslov index | stability of travelling waves | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Stability | Inhibitors | Planes | Eigenvalues | Traveling waves | Conjugate points | Eigen values

Journal Article

1995, Lecture notes in mathematics, ISBN 0387600477, Volume 1609, vi, 329

This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June...

Differentiable dynamical systems | Global analysis (Mathematics) | Systems theory | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Mathematical optimization | Analysis

Differentiable dynamical systems | Global analysis (Mathematics) | Systems theory | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Mathematical optimization | Analysis

Book

Transactions of the American Mathematical Society, ISSN 0002-9947, 2016, Volume 368, Issue 11, pp. 8145 - 8207

We study the Schrodinger operator L = -Delta + V on a star-shaped domain Omega in R-d with Lipschitz boundary partial derivative Omega. The operator is...

Eigenvalues | Hamiltonian systems | Differential operators | Stability | Schrödinger equation | Physical Sciences | Mathematics | Science & Technology

Eigenvalues | Hamiltonian systems | Differential operators | Stability | Schrödinger equation | Physical Sciences | Mathematics | Science & Technology

Journal Article

Physica. D, ISSN 0167-2789, 02/2015, Volume 292-293, pp. 70 - 83

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data...

Mixed-mode oscillations | Paleoclimate | Glacial cycle | MMO | Fast/slow | Folded node | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology | Case studies | Climate | Climate models | Knowledge | Analysis | Relaxation oscillations | Oscillations | Mathematical models | Stores | Carbon | Atmospherics | Oscillators | Mathematics - Dynamical Systems

Mixed-mode oscillations | Paleoclimate | Glacial cycle | MMO | Fast/slow | Folded node | Physical Sciences | Physics, Fluids & Plasmas | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Mathematics, Applied | Physics | Science & Technology | Case studies | Climate | Climate models | Knowledge | Analysis | Relaxation oscillations | Oscillations | Mathematical models | Stores | Carbon | Atmospherics | Oscillators | Mathematics - Dynamical Systems

Journal Article

SIAM journal on control and optimization, ISSN 0363-0129, 2017, Volume 55, Issue 2, pp. 741 - 759

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter...

Linear dynamics | Rank | Control theory | Covariance matrix | Kalman filter | Data assimilation | Automation & Control Systems | Physical Sciences | Mathematics | Mathematics, Applied | Technology | Science & Technology

Linear dynamics | Rank | Control theory | Covariance matrix | Kalman filter | Data assimilation | Automation & Control Systems | Physical Sciences | Mathematics | Mathematics, Applied | Technology | Science & Technology

Journal Article

Communications in partial differential equations, ISSN 0360-5302, 08/2015, Volume 40, Issue 8, pp. 1467 - 1497

Given a selfadjoint, elliptic operator L, one would like to know how the spectrum changes as the spatial domain Ω ⊂ ℝ
n
is deformed. For a family of domains {Ω...

Morse index | Secondary: 53D12 | Domain deformation | Elliptic boundary value problem | Maslov index | Primary: 35P15 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Partial differential equations | Operators | Theorems | Spectral theory | Dirichlet problem | Boundary conditions | Boundaries | Subspaces

Morse index | Secondary: 53D12 | Domain deformation | Elliptic boundary value problem | Maslov index | Primary: 35P15 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Partial differential equations | Operators | Theorems | Spectral theory | Dirichlet problem | Boundary conditions | Boundaries | Subspaces

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 12/2014, Volume 257, Issue 12, pp. 4632 - 4703

This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein–Gordon equation...

Spectral stability | Modulation theory | Nonlinear Klein–Gordon equation | Periodic wavetrains | Nonlinear Klein-Gordon equation | Physical Sciences | Mathematics | Science & Technology

Spectral stability | Modulation theory | Nonlinear Klein–Gordon equation | Periodic wavetrains | Nonlinear Klein-Gordon equation | Physical Sciences | Mathematics | Science & Technology

Journal Article