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