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References (44)
-
Christopher Knight, G. Derks, A. Doelman, H. Susanto (2013)
Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneityJournal of Differential Equations, 254
-
M. Grillakis, J. Shatah, W. Strauss (1990)
Stability theory of solitary waves in the presence of symmetry, II☆Journal of Functional Analysis, 94
-
A.N. Vystavkin, Yu.F. Drachevskii, V.P. Koshelets, I.L. Serpuchenko (1988)
First observation of static bound states of fluxons in long Josephson junctions with inhomogeneitiesSov. J. Low Temp. Phys., 14
-
G. Griffiths, W. Schiesser (2009)
Linear and nonlinear wavesScholarpedia, 4
-
Yoshimi Saito (1971)
Eigenfunction Expansions Associated with Second-order Differential Equations for Hilbert Space-valued FunctionsPublications of The Research Institute for Mathematical Sciences, 7
-
(1999)
Introduction to Mechanics and Symmetry, 2nd edn -
Roy Goodman, R. Haberman (2007)
Chaotic scattering and the n-bounce resonance in solitary-wave interactions.Physical review letters, 98 10
-
Y. Kivshar, Z. Fei, Luis Vázquez (1991)
Resonant soliton-impurity interactions.Physical review letters, 67 10
-
P. Heijster, A. Doelman, T. Kaper, Y. Nishiura, Kei-Ichi Ueda (2010)
Pinned fronts in heterogeneous media of jump typeNonlinearity, 24
-
Wolfgang Hackbusch (2014)
Ordinary Differential Equations -
I. Serpuchenko, A. Ustinov (1987)
Experimental observation of fine structure on the current-voltage characteristics of long Josephson junctions with a lattice of inhomogeneitiesJetp Letters, 46
-
Xiaohui Yuan, T. Teramoto, Y. Nishiura (2007)
Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reaction-diffusion system.Physical review. E, Statistical, nonlinear, and soft matter physics, 75 3 Pt 2
-
J.E. Marsden, T.S. Ratiu (1999)
Introduction to Mechanics and Symmetry -
M. Weides, M. Kemmler, H. Kohlstedt, R. Waser, D. Koelle, R. Kleiner, E. Goldobin (2006)
0-pi Josephson tunnel junctions with ferromagnetic barrier.Physical review letters, 97 24
-
M. Plaza, J. Stubbe, L. Vázquez (1990)
Existence and stability of travelling waves in (1+1) dimensionsJournal of Physics A, 23
-
G. Derks, A. Doelman, Christopher Knight, H. Susanto (2011)
Pinned fluxons in a Josephson junction with a finite-length inhomogeneityEuropean Journal of Applied Mathematics, 23
-
R. Marangell, H. Susanto, C. Jones (2012)
Unstable gap solitons in inhomogeneous nonlinear Schrödinger equationsJournal of Differential Equations, 253
-
M. Weides, H. Kohlstedt, R. Waser, M. Kemmler, J. Pfeiffer, D. Koelle, R. Kleiner, E. Goldobin (2007)
Ferromagnetic 0−π Josephson junctionsAppl. Phys. A, Mater. Sci. Process., 89
-
Y. Kivshar, B. Malomed (1989)
Dynamics of Solitons in Nearly Integrable SystemsReviews of Modern Physics, 61
-
P. Teodorescu, L. Munteanu (2008)
On the solitons and nonlinear wave equations -
Y. Kivshar, A. Kosevich, O. Chubykalo (1988)
Finite-size effects in fluxon scattering by an inhomogeneityPhysics Letters A, 129
-
D. McLaughlin, A. Scott (1978)
Perturbation analysis of fluxon dynamicsPhysical Review A, 18
-
E.C. Titchmarsh (1962)
Eigenfunction Expansions Associated with Second-Order Differential Equations -
Roy Goodman, M. Weinstein (2007)
Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical studyPhysica D: Nonlinear Phenomena, 237
-
Christopher Knight, G. Derks (2014)
A stability criterion for the non-linear wave equation with spatial inhomogeneityarXiv: Pattern Formation and Solitons
-
S. Scharinger, C. Gürlich, R. Mints, M. Weides, H. Kohlstedt, E. Goldobin, D. Koelle, R. Kleiner (2010)
Interference patterns of multifacet 20× (0-π) Josephson junctions with ferromagnetic barrierPhysical Review B, 81
-
C. Jones (1988)
Instability of standing waves for non-linear Schrödinger-type equationsErgodic Theory and Dynamical Systems, 8
-
C. Jones, J. Moloney (1986)
Instability of standing waves in nonlinear optical waveguidesPhysics Letters A, 117
-
P. Heijster, A. Doelman, T. Kaper, K. Promislow (2010)
Front Interactions in a Three-Component SystemSIAM J. Appl. Dyn. Syst., 9
-
Roy Goodman, R. Haberman (2003)
Interaction of sine-Gordon kinks with defects: the two-bounce resonancePhysica D: Nonlinear Phenomena, 195
-
H. Akoh, S. Sakai, A. Yagi, H. Hayakawa (1985)
Real time fluxon dynamics in josephson transmission lineIEEE Transactions on Magnetics, 21
-
A. Barone, F. Esposito, C. Magee, A. Scott (1971)
Theory and applications of the sine-gordon equationLa Rivista del Nuovo Cimento (1971-1977), 1
-
L. I︠A︡kushevich (1998)
Nonlinear Physics of DNA -
R.K. Jackson, R. Marangell, H. Susanto (2014)
An instability criterion for standing waves on nonzero backgroundsJ. Nonlinear Sci.
-
M. Weides, H. Kohlstedt, R. Waser, M. Kemmler, J. Pfeiffer, D. Koelle, R. Kleiner, E. Goldobin (2007)
Ferromagnetic 0–π Josephson junctionsApplied Physics A, 89
-
G. Derks, G. Gaeta (2011)
A minimal model of DNA dynamics in interaction with RNA-PolymerasePhysica D: Nonlinear Phenomena, 240
-
(2005)
Theory of nonlinear Schrödinger equations and selection of the ground state -
B. Piette, W. Zakrzewski (2006)
Dynamical properties of a soliton in a potential wellJournal of Physics A: Mathematical and Theoretical, 40
-
(1978)
Solitons and Condensed Matter Physics: Proceedings of a Symposium Held June 27–29 -
R. Marangell, R. Marangell, Christopher Jones, Christopher Jones, Hadi Susanto (2010)
Localized standing waves in inhomogeneous Schrödinger equationsNonlinearity, 23
-
A. Davydov (1979)
Solitons in molecular systems -
J. Gibbon, I. James, I. Moroz (1979)
The Sine-Gordon Equation as a Model for a Rapidly Rotating Baroclinic FluidPhysica Scripta, 20
-
(1985)
Fluxon transfer devices -
R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, H.C. Morris (1982)
Solitons and Nonlinear Wave Equations
- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Springer Science+Business Media Dordrecht
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-014-9991-z
- Publisher site
- See Article on Publisher Site
Abstract
This paper presents an introduction to the existence and stability of stationary fronts in wave equations with finite length spatial inhomogeneities. The main focus will be on wave equations with one or two inhomogeneities. It will be shown that the fronts come in families. The front solutions provide a parameterisation of the length of the inhomogeneities in terms of the local energy of the potential in the inhomogeneity. The stability of the fronts is determined by analysing (constrained) critical points of those length functions. Amongst others, it will shown that inhomogeneities can stabilise non-monotonic fronts. Furthermore it is demonstrated that bi-stability can occur in such systems.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 4, 2014