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Lecture Note Sketches Hermann Riecke - ESAM Home Page

Lecture Note Sketches Hermann Riecke - ESAM Home Page

Index beating, 20

Index beating, 20 conserved quantity, 78 continuous family, 81 convection, 86 critical droplet, 96 detuning, 10 Fredholm Alternative Theorem, 29 functional derivative, 77 generalized eigenvectors, 83 generalized Fourier integral, 60 Goldstone modes, 83 harmonic response, 11 heteroclinic, 87 homoclinic, 87 Hopf bifurcation, 24 I(x)=\int {0}ˆ{1}eˆ{ixtˆ{2}}dt, 65 I(x)=\int {0}ˆ{1}\frac{1}{t}\sin xt\, dts, 44 I(x)=\int {0}ˆ{1}\frac{eˆ{ixt}}{1+t}dt, 60 I(x)=\int {0}ˆ{1}\ln t\, eˆ{ixt}dt, 64 I(x)=\int {0}ˆ{1}\sqrt{t}eˆ{ixt}, 61 I(x)=\int {0}ˆ{a}\left(1-t\right)ˆ{-1}eˆ{-xt}dt, 51 I(x)=\int {0}ˆ{\frac{\pi}{2}}eˆ{-x\sinˆ{2}t}dt, 59 I(x)=\int {0}ˆ{\infty}\cos\left(xtˆ{2}-t\right)dt, 63 I(x)=\int {0}ˆ{\infty}eˆ{-\frac{1}{t}}eˆ{-xt}dt, 56 I(x)=\int {0}ˆ{\infty}\frac{eˆ{-t}}{1+xt}dt, 49 I(x)=\int {0}ˆ{\pi/2}eˆ{-x\sinˆ{2}t}dt, 55 I(x)=\int {0}ˆ{x}tˆ{-\frac{1}{2}}eˆ{-t}dt, 48 I(x)=\int {x}ˆ{\infty}eˆ{-tˆ{4}}dt, 48 I(x)=\int {x}ˆ{\infty}tˆ{a-1}eˆ{-t}\, dt, 44 I {n}(x)=\frac{1}{\pi}\int {0}ˆ{\pi}eˆ{x\cos t}\cos nt\, dt, 56 integrable, 79 K {0}(x)=\int {1}ˆ{\infty}\left(sˆ{2}-1\right)ˆ{- 1/2}eˆ{-xs}ds, 53 4 localized wave, 88 Lyapunov functional, 78 movable maximum, 57 pitch-fork bifurcation, 85 scalar product, 29 spatially chaotic, 97 Stokes lines, 74 Stokes phenomenon, 72 subdominant, 51 subharmonic, 10, 16 topologically stable, 87 translation modes, 83 unstable, 16

References [1] P. Coullet, C. Elphick, and D. Repaux. Nature of spatial chaos. Phys. Rev. Lett., 58:431– 434, 1987. [2] T Dauxois, M Peyrard, and S Ruffo. The Fermi-Pasta-Ulam ‘numerical experiment’: history and pedagogical perspectives. Eur. J. Physics, 26(5):S3–S11, SEP 2005. [3] P. Kolodner, D. Bensimon, and C. Surko. Traveling-wave convection in an annulus. Phys. Rev. Lett., 60:1723, 1988. [4] P. Kolodner, J.A. Glazier, and H. Williams. Dispersive chaos in one-dimensional traveling-wave convection. Phys. Rev. Lett., 65:1579, 1990. [5] P. Kolodner, S. Slimani, N. Aubry, and R. Lima. Characterization of dispersive chaos and related states of binary-fluid convection. Physica D, 85(1-2):165–224, July 1995. [6] B.A. Malomed and A.A. Nepomnyashchy. Kinks and solitons in the generalized Ginzburg-Landau equation. Phys. Rev. A, 42:6009, 1990. [7] O. Thual and S. Fauve. Localized structures generated by subcritical instabilities. J. Phys. (Paris), 49:1829, 1988. [8] NJ Zabusky. Fermi-Pasta-Ulam, solitons and the fabric of nonlinear and computational science: History, synergetics, and visiometrics. CHAOS, 15(1), MAR 2005. 5

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