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Kink dynamics in one-dimensional nonlinear systems
Kyozi Kawasaki,Takao Ohta +1 more
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TLDR
In this article, a special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics, which corresponds to the momentum conservation law for wave equations.Abstract:
A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.read more
Citations
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Instabilities in crystal growth by atomic or molecular beams
TL;DR: In this paper, a review of the most frequent instabilities in ballistic growth is presented, which are mostly kinetic (when the desired state cannot be reached because of a lack of time) or thermodynamic (when a desired state is unstable).
Journal ArticleDOI
Pattern formation in non-gradient reaction-diffusion systems: the effects of front bifurcations
Aric Hagberg,Ehud Meron +1 more
TL;DR: In this paper, a symmetry breaking front bifurcation is studied in a wide class of reaction-diffusion systems and the effects it has on pattern formation and pattern dynamics.
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Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations
TL;DR: An extended parameter range of multistability of the pinning and coarsening morphologies is obtained and it is shown that the instability to transversal modes leading to a decay of the ridges into rows of drops may diminish the size of the parameter range where the pining of the thin film to the template is successful.
Journal ArticleDOI
Higher-dimensional localized patterns in excitable media
TL;DR: In this paper, it is shown that a band-shaped localized pattern is destabilized into a zig-zag mode or a varicose mode and that a disk-shaped local pattern, when τ is small, into an oscillatory mode like a "breather motion".
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The Motion of Weakly Interacting Pulses in Reaction-Diffusion Systems
TL;DR: In this article, an attractive local invariant manifold is constructed to give the dynamics of interacting pulses in a mathematically rigorous way, and the equations describing the flow on the manifold are also given in an explicit form.
References
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Journal ArticleDOI
Dynamics of classical solitons (in non-integrable systems)
TL;DR: A survey of the properties of soliton-type solutions to non-linear wave equations appearing in various fields of physics is given in this paper, where the results of computer experiments on the dynamics of the formation and interaction (in one-space-dimensional geometry) of solit-type objects are presented at length.
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Theory of spinodal decomposition in alloys
TL;DR: In this paper, a statistical theory of the thermally driven composition fluctuations in a binary alloy is developed for the purpose of studying the phenomenon of spinodal decomposition, which can be stated in the form of a Fokker-Planck equation, which reduces, upon taking a suitable moment, to the nonlinear generalized diffusion equation.
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Studies of a non-linear lattice
TL;DR: In this paper, an exact treatment of the propagation of waves in one-dimensional non-linear lattices is presented, and particular solutions of the equations of motion are given in analytic form, and are shown to have wide applicabilities in elucidating general features of nonlinear waves.
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Kinetic Drumhead Model of Interface. I
Kyozi Kawasaki,Takao Ohta +1 more
TL;DR: In this paper, the Euclidean invariant stochastic equation of motion for the coordinate of the interface is derived systematically from the time-dependent Ginzburg-Landau model in the limit of infinitely deep potential well of the order parameter.