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Books
T. Kapitula and K. Promislow
Spectral and Dynamical Stability of Nonlinear Waves (Springer E-book, Amazon.com)
Springer (2013)
T. Kapitula
Ordinary Differential Equations and Linear Algebra: A Systems Approach (SIAM book page)
SIAM (2015)
Undergraduate Student Research
K. Eekhoff
Opinion formation dynamics with contrarians and zealots
SIAM Undergraduate Research Online 12 (2019)
J. Bujalski, G. Dwyer, T. Kapitula, Q.-N. Le, H. Malvai, J. Rosenthal-Kay, and J. Ruiter
Consensus and clustering in opinion formation on networks
Phil. Trans. Royal Society A 376: 20170186 (2018)
M. Morrissey and J. Collignon
Propagation of lead in the human body
SIAM Undergraduate Research Online 10 (2017)
R. Coggin
Numerically computing zeros of the Evans Function (MATLAB files)
SIAM Undergraduate Research Online 8 (2015)
S. Auyeung and E. Yu
The Krein matrix and an Interlacing Theorem
SIAM Undergraduate Research Online 7 (2014)
T. Kapitula, E. Hibma, H.-P. Kim, and J. Timkovich
Instability indices for matrix polynomials
Linear Algebra Appl. 439(11):3412-3434 (2013)
J. Christiansen
Finding eigenvalues for matrices acting on subspaces
SIAM Undergraduate Research Online 5 (2012)
B. Lewis
Tracking the movement of eigenvalues via a corresponding Evans function
SIAM Undergraduate Research Online 5 (2012)
T. Kapitula, N. De Jong, and K. Plaisier
Wave dynamics in the extended forced KdV
SIAM J. Appl. Math. 71(3):811-828 (2011)
Peer Reviewed Journal Articles
T. Kapitula, P. Kevrekidis, and H. Xu
Existence, stability, and dynamics of harmonically trapped one-dimensional multi-component solitary waves: the near-linear limit
J. Math. Physics 58061901 (2017)
B. Deconinck and T. Kapitula
On the spectral and orbital stability of spatially periodic stationary solutions of generalized Korteweg-de Vries equations
Hamiltonian Partial Diff. Eq. Appl. 75:285-322 (2015)
A. Demirkaya, M. Stanislavova, A. Stefanov, T. Kapitula, and P. Kevrekidis
On the spectral stability of kinks in some PT-symmetric variants of the classical Klein-Gordon field theories
Studies Appl. Math. 133:298-317 (2014)
J. Bronski, M. Johnson, and T. Kapitula
An instability index theory for quadratic pencils and applications
Comm. Math. Physics 327(2):521-550 (2014)
A. Stefanov and T. Kapitula
A Hamiltonian-Krein (instability) index theory for KdV-like eigenvalue problems
Studies Appl. Math. 132:183-211 (2014)
M. Haragus and T. Kapitula
Spots and stripes in nonlinear Schrodinger-type equations with nearly one-dimensional potentials
Math. Methods Appl. Sci. 37(1):75-94 (2014)
T. Kapitula, P. Kevrekidis, and D. Yan
The Krein Matrix: General Theory and Concrete Applications in Atomic Bose-Einstein Condensates
SIAM J. Appl. Math. 73(4):1368-1395 (2013)
T. Kapitula and K. Promislow
Stability indices for constrained self-adjoint operators
Proc. Amer. Math. Soc. 140(3):865-880 (2012)
J. Bronski, M. Johnson, and T. Kapitula
An index theorem for the stability of periodic traveling waves of KdV type
Proc. Roy. Soc. Edinburgh: Section A 141(6):1141-1173 (2011)
T. Kapitula
The Krein signature, Krein eigenvalues, and the Krein Oscillation Theorem
Indiana U. Math. J. 59(4):1245-1276 (2010)
B. Deconinck and T. Kapitula
The orbital stability of the cnoidal waves of the Korteweg-de Vries equation
Phys. Letters A 374:4018-4022 (2010)
T. Kapitula, K. Law, and P. Kevrekidis
Interaction of excited states in two-species Bose-Einstein condensates: a case study
SIAM J. Appl. Dyn. Sys. 9(1):34-61 (2010)
M. Haragus and T. Kapitula
On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
Physica D 237(20):2649-2671 (2008)
T. Kapitula, P. Kevrekidis, and D. Frantzeskakis
Disk-shaped Bose-Einstein condensates in the presence of an harmonic trap and an optical lattice (.pdf)
Chaos 18(2):023101 (2008)
T. Kapitula, P. Kevrekidis, and R. Carretero-Gonzalez
Rotating matter waves in Bose-Einstein condensates
Physica D 233(2):112-137 (2007)
T. Kapitula
On the stability of N-solitons in integrable systems
Nonlinearity 20(4):879-907 (2007)
T. Kapitula, P. Kevrekidis, and Z. Chen
Three is a crowd: Solitary waves in photorefractive media with three potential wells
SIAM J. Appl. Dyn. Sys. 5(4):598-633 (2006)
T. Kapitula and P. Kevrekidis
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice
Chaos 15(3):037114 (2005)
T. Kapitula and P. Kevrekidis
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice: two-mode approximation
Nonlinearity 18(6):2491-2512 (2005)
T. Kapitula, P. Kevrekidis, and B. Sandstede
Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
Physica D 201(1&2):199-201 (2005)
T. Kapitula, P. Kevrekidis, and B. Sandstede
Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
Physica D 195(3&4):263-282 (2004)
T. Kapitula, J. N. Kutz, and B. Sandstede
The Evans function for nonlocal equations
Indiana U. Math. J. 53(4):1095-1126 (2004)
T. Kapitula and P. Kevrekidis
Linear stability of perturbed Hamiltonian systems: theory and a case example
J. Phys. A: Math. Gen. 37(30):7509-7526 (2004)
T. Kapitula and B. Sandstede
Edge bifurcations for near integrable systems via Evans-function techniques
SIAM J. Math. Anal. 33(5):1117-1143 (2002)
T. Kapitula, J. N. Kutz, and B. Sandstede
Stability of pulses in the master-modelocking equation
J. Opt. Soc. Am. B 19(4):740-746 (2002)
T. Kapitula
Stability of waves in perturbed Hamiltonian systems
Physica D 156(1&2):186-200 (2001)
T. Kapitula and P. Kevrekidis
Stability of waves in discrete systems
Nonlinearity 14(3):533-566 (2001)
T. Kapitula, P. Kevrekidis, and C.K.R.T. Jones
Soliton internal mode bifurcations: Pure power law?
Phys. Rev. E 63(3):036602 (2001)
T. Kapitula, P. Kevrekidis, and Boris Malomed
Stability of multiple pulses in discrete systems
Phys. Rev. E 63(3):036604 (2001)
P. Kevrekidis, C.K.R.T. Jones, and T. Kapitula
Exponentially small splitting of heteroclinic orbits: from the rapidly forced pendulum to discrete solitons
Phys. Lett. A 269(2-3):120-129 (2000)
T. Kapitula and J. Rubin
Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
Nonlinearity 13(1):77-112 (2000)
T. Kapitula
The Evans function and generalized Melnikov integrals
SIAM J. Math. Anal. 30(2):273-297 (1999)
T. Kapitula and B. Sandstede
Stability of bright solitary-wave solutions to perturbed nonlinear Schrodinger equations
Physica D 124(1-3):58-103 (1998)
T. Kapitula and B. Sandstede
A novel instability mechanism for bright solitary-wave solutions to the cubic-quintic Ginzburg-Landau equation
J. Opt. Soc. Am. B 15:2757-2762 (1998)
T. Kapitula
Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrodinger equation
Proc. Roy. Soc. Edinburgh A 128(3):585-629 (1998)
T. Kapitula
Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrodinger equation
Physica D 116(1-2):95-120 (1998)
T. Kapitula
Multidimensional stability of planar travelling waves
Trans. American Math. Soc. 349(1):257-269 (1997)
T. Kapitula
Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation
Nonlinearity 9:669-685 (1996)
T. Kapitula and S. Maier-Paape
Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation
Z angew Math. Phys. 47:265-305 (1996)
T. Kapitula
Singular heteroclinic orbits for degenerate modulation equations
Physica D 82:36-59 (1995)
T. Kapitula
On the stability of travelling waves in weighted L^\infty spaces
J. Diff. Eq. 112(1):179-215,(1994)
T. Kapitula
On the nonlinear stability of plane waves for the Ginzburg-Landau equation
Comm. Pure Appl. Math. 47:831-841 (1994)
C.K.R.T. Jones, R. Gardner, and T. Kapitula
Stability of travelling waves for non-convex scalar viscous conservation laws
Comm. Pure Appl. Math. 46:505-526 (1993)
T. Kapitula
Stability of weak shocks in lambda-omega systems
Indiana U. Math. J. 40(4):1193-1219 (1991)
C.K.R.T. Jones, T. Kapitula, and J. Powell
Nearly real fronts in a Ginzburg-Landau equation
Proc. Roy. Soc. Edinburgh 116A:193-206 (1990)
Review Articles
T. Kapitula
Stability analysis of pulses via the Evans function: dissipative systems (.pdf)
A chapter in the book entitled "Dissipative Solitons"
Lecture Notes in Physics 661:407-427 (2005)
T. Kapitula and B. Sandstede
Eigenvalues and resonances using the Evans function
Discrete and Continuous Dynamical Systems 10(4):857-869 (2004)
| Last updated 12/05/2019 |