-
5
-
-
30644464329
-
Micro-macro transition for the atomic chain via Whitham's modulation equation
-
W. Dreyer, M. Herrmann, and A. Mielke. Micro-macro transition for the atomic chain via Whitham's modulation equation. Nonlinearity, 19(2), 471-500, 2006.
-
(2006)
Nonlinearity
, vol.19
, Issue.2
, pp. 471-500
-
-
Dreyer, W.1
Herrmann, M.2
Mielke, A.3
-
6
-
-
0039600839
-
Cold, thermal and oscillator closure of the atomic chain
-
W. Dreyer and M. Kunik. Cold, thermal and oscillator closure of the atomic chain. J. Phys. A: Math. Gen., 33, 2097-2129, 2000.
-
(2000)
J. Phys. A: Math. Gen.
, vol.33
, pp. 2097-2129
-
-
Dreyer, W.1
Kunik, M.2
-
7
-
-
25344451956
-
The Toda lattice II. Existence of integrals
-
P. Deift, S. Kamvissis, T. Kriecherbauer, and X. Zhou. The Toda lattice ii. existence of integrals. Phys. Rev. B, 9(4), 1924-1925, 1974.
-
(1974)
Phys. Rev. B
, vol.9
, Issue.4
, pp. 1924-1925
-
-
Deift, P.1
Kamvissis, S.2
Kriecherbauer, T.3
Zhou, X.4
-
8
-
-
0030539847
-
The Toda rarefaction problem
-
P. Deift, S. Kamvissis, T. Kriecherbauer, and X. Zhou. The Toda rarefaction problem. Comm. Pure Appl. Math, 49(1), 35-83, 1996.
-
(1996)
Comm. Pure Appl. Math
, vol.49
, Issue.1
, pp. 35-83
-
-
Deift, P.1
Kamvissis, S.2
Kriecherbauer, T.3
Zhou, X.4
-
9
-
-
0039991128
-
Forced lattice vibrations, Part I
-
P. Deift, T. Kriecherbauer, and S. Venakides. Forced lattice vibrations, Part I. Comm. Pure Appl. Math., 48, 1187-1250, 1995.
-
(1995)
Comm. Pure Appl. Math.
, vol.48
, pp. 1187-1250
-
-
Deift, P.1
Kriecherbauer, T.2
Venakides, S.3
-
11
-
-
20444489898
-
Resolution of a shock in hyperbolic systems modified by weak dispersion
-
G. El. Resolution of a shock in hyperbolic systems modified by weak dispersion. Chaos, 15, 2005.
-
Chaos
, vol.15
, pp. 2005
-
-
El, G.1
-
12
-
-
0001306661
-
Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization
-
S. Flach. Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization. Physica D, 91, 223-243, 1996.
-
(1996)
Physica D
, vol.91
, pp. 223-243
-
-
Flach, S.1
-
13
-
-
0036836750
-
Atomic-scale localization of high-energy solitary waves on lattices
-
G. Friesecke and K. Matthies. Atomic-scale localization of high-energy solitary waves on lattices. Physica D, 171, 211-220, 2002.
-
(2002)
Physica D
, vol.171
, pp. 211-220
-
-
Friesecke, G.1
Matthies, K.2
-
14
-
-
0042762774
-
Geometric solitary waves in a 2d mass spring lattice. Discrete Contin
-
G. Friesecke and K. Matthies. Geometric solitary waves in a 2d mass spring lattice. Discrete Contin. Dyn. Syst. Ser. B, 3, 105-114, 2003.
-
(2003)
Dyn. Syst. Ser. B
, vol.3
, pp. 105-114
-
-
Friesecke, G.1
Matthies, K.2
-
15
-
-
0033229031
-
Solitary waves on FPU lattices. I. Qualitative properties, renormalization and continuum limit
-
G. Friesecke and R. L. Pego. Solitary waves on FPU lattices. I. Qualitative properties, renormalization and continuum limit. Comm. Math. Phys., 12(6), 1601-1627, 1999.
-
(1999)
Comm. Math. Phys.
, vol.12
, Issue.6
, pp. 1601-1627
-
-
Friesecke, G.1
Pego, R.L.2
-
17
-
-
0033449491
-
Existence and modulation of traveling waves in particle chains
-
A.-M. Filip and S. Venakides. Existence and modulation of traveling waves in particle chains. Comm. Pure Appl. Math., 51(6), 693-735, 1999.
-
(1999)
Comm. Pure Appl. Math.
, vol.51
, Issue.6
, pp. 693-735
-
-
Filip, A.-M.1
Venakides, S.2
-
18
-
-
21344488602
-
Existence theorem for solitary waves on lattices
-
G. Friesecke and J. A. D. Wattis. Existence theorem for solitary waves on lattices. Comm. Math. Phys., 161(2), 391-418, 1994.
-
(1994)
Comm. Math. Phys.
, vol.161
, Issue.2
, pp. 391-418
-
-
Friesecke, G.1
Wattis, J.A.D.2
-
19
-
-
38849166067
-
Continuum descriptions for the dynamics in discrete lattices: Derivation and justification
-
A. Mielke edr, Springer-Verlag
-
J. Giannoulis, M. Herrmann, and A. Mielke. Continuum descriptions for the dynamics in discrete lattices: derivation and justification. In "Analysis, Modeling and Simulation of Multiscale Problems, A. Mielke (edr), Springer-Verlag, 2006.".
-
(2006)
Analysis, Modeling and Simulation of Multiscale Problems
-
-
Giannoulis, J.1
Herrmann, M.2
Mielke, A.3
-
21
-
-
84990622676
-
On dispersive difference schemes
-
J. Goodman and P. Lax. On dispersive difference schemes. Comm. Pure. Appl. Math., 41, 591-613, 1988.
-
(1988)
Comm. Pure. Appl. Math.
, vol.41
, pp. 591-613
-
-
Goodman, J.1
Lax, P.2
-
22
-
-
1642318760
-
The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities
-
J. Giannoulis and A. Mielke. The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities. Nonlinearity, 17, 551-565, 2004.
-
(2004)
Nonlinearity
, vol.17
, pp. 551-565
-
-
Giannoulis, J.1
Mielke, A.2
-
23
-
-
33745240977
-
Dispersive evolution of pulses in oscillator chains with general interaction potentials
-
J. Giannoulis and A. Mielke. Dispersive evolution of pulses in oscillator chains with general interaction potentials. Discr. Cont. Dynam. Systems Ser. B, 6, 493-523, 2006.
-
(2006)
Discr. Cont. Dynam. Systems Ser. B
, vol.6
, pp. 493-523
-
-
Giannoulis, J.1
Mielke, A.2
-
24
-
-
0001600405
-
Integrals of the Toda lattice
-
M. Hénon. Integrals of the Toda lattice. Phys. Rev. B, 9(4), 1921-1923, 1974.
-
(1974)
Phys. Rev. B
, vol.9
, Issue.4
, pp. 1921-1923
-
-
Hénon, M.1
-
26
-
-
0001396098
-
Shock waves in the toda lattice: Analysis
-
B. Holian, H. Flaschka, and D. McLaughlin. Shock waves in the toda lattice: Analysis. Phys. Rev. A, 24(5), 2595-2623, 1981.
-
(1981)
Phys. Rev. A
, vol.24
, Issue.5
, pp. 2595-2623
-
-
Holian, B.1
Flaschka, H.2
McLaughlin, D.3
-
27
-
-
84990609933
-
Dispersive approximations in fluid dynamics
-
T. Y. Hou and P. Lax. Dispersive approximations in fluid dynamics. Comm. Pure Appl. Math., 44, 1-40, 1991.
-
(1991)
Comm. Pure Appl. Math.
, vol.44
, pp. 1-40
-
-
Hou, T.Y.1
Lax, P.2
-
28
-
-
0040753984
-
Macroscopic lattice dynamics
-
M. Hays, C. D. Levermore, and P. Miller. Macroscopic lattice dynamics. Physica D, 79(1), 1-15, 1994.
-
(1994)
Physica D
, vol.79
, Issue.1
, pp. 1-15
-
-
Hays, M.1
Levermore, C.D.2
Miller, P.3
-
29
-
-
0003835647
-
-
Mathem. Springer, Berlin
-
E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration, volume 31 of Springer Series in Comp. Mathem. Springer, Berlin, 2002.
-
(2002)
Geometric Numerical Integration, Volume 31 of Springer Series in Comp
-
-
Hairer, E.1
Lubich, C.2
Wanner, G.3
-
32
-
-
0036434955
-
Zero diffusion-dispersion limits for hyperbolic conservation laws
-
C. Kondo and P. Le Floch. Zero diffusion-dispersion limits for hyperbolic conservation laws. SIAM Math. Anal., 22, 1320-1329, 2002.
-
(2002)
SIAM Math. Anal.
, vol.22
, pp. 1320-1329
-
-
Kondo, C.1
Le Floch, P.2
-
33
-
-
25044440100
-
A uniqueness criterion for the Riemann problem
-
P. Krejçi and I. Straşkraba. A uniqueness criterion for the Riemann problem. Hiros. Math. J., 27, 307-346, 1997.
-
(1997)
Hiros. Math. J.
, vol.27
, pp. 307-346
-
-
Krejçi, P.1
Straşkraba, I.2
-
34
-
-
84971162773
-
The validity of modulation equations for extended systems with cubic nonlinearities
-
P. Kirrmann, G. Schneider, and A. Mielke. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A, 122, 85-91, 1992.
-
(1992)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.122
, pp. 85-91
-
-
Kirrmann, P.1
Schneider, G.2
Mielke, A.3
-
35
-
-
0039031951
-
On dispersive difference schemes
-
P. Lax. On dispersive difference schemes. Physica D, 18, 250-254, 1986.
-
(1986)
Physica D
, vol.18
, pp. 250-254
-
-
Lax, P.1
-
36
-
-
84990564068
-
The zero dispersion limit, a deterministic analogue of turbulence
-
P. Lax. The zero dispersion limit, a deterministic analogue of turbulence. Comm. Pure Appl. Math., 44, 1047-1056, 1991.
-
(1991)
Comm. Pure Appl. Math.
, vol.44
, pp. 1047-1056
-
-
Lax, P.1
-
38
-
-
84990575581
-
The small dispersion limit of the Korteweg-de Vries equation, I, II, III
-
no. 5, 571-593; no. 6, 809-830
-
P. Lax and C. Levermore. The small dispersion limit of the Korteweg-de Vries equation, I, II, III. omm. Pure Appl. Math., 36, no. 3, 253-290; no. 5, 571-593; no. 6, 809-830, 1983.
-
(1983)
Omm. Pure Appl. Math.
, vol.36
, Issue.3
, pp. 253-290
-
-
Lax, P.1
Levermore, C.2
-
39
-
-
0030384290
-
Large oscillations arising in a dispersive numerical scheme
-
C. Levermore and J. Liu. Large oscillations arising in a dispersive numerical scheme. Physica D, 99, 191-216, 1996.
-
(1996)
Physica D
, vol.99
, pp. 191-216
-
-
Levermore, C.1
Liu, J.2
-
40
-
-
0012009827
-
The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior
-
A. Fokas and V. Zakharov, editors, Springer, Berlin
-
P. D. Lax, C. D. Levermore, and S. Venakides. The generation and propagation of oscillations in dispersive initial value problems and their limiting behavior. In A. Fokas and V. Zakharov, editors, Important developments in soliton theory, pages 205-241. Springer, Berlin, 1993.
-
(1993)
Important Developments in Soliton Theory
, pp. 205-241
-
-
Lax, P.D.1
Levermore, C.D.2
Venakides, S.3
-
43
-
-
14944346675
-
Wigner measures in the discrete setting: High-frequency analysis of sampling and reconstruction operators
-
F. Maciá. Wigner measures in the discrete setting: high-frequency analysis of sampling and reconstruction operators. SIMA, 36(2), 347-383, 2004.
-
(2004)
SIMA
, vol.36
, Issue.2
, pp. 347-383
-
-
Maciá, F.1
-
44
-
-
67649370945
-
The Ginzburg-Landau equation in its role as a modulation equation
-
B. Fiedler, editor, Elsevier Science B. V.
-
A. Mielke. The Ginzburg-Landau equation in its role as a modulation equation. In B. Fiedler, editor, Handbook of Dynamical Systems II, pages 759-834. Elsevier Science B. V., 2002.
-
(2002)
Handbook of Dynamical Systems II
, pp. 759-834
-
-
Mielke, A.1
-
45
-
-
33745585326
-
Macroscopic behavior of microscopic oscillations in harmonic lattices using wigner-husimi measures
-
A. Mielke. Macroscopic behavior of microscopic oscillations in harmonic lattices using wigner-husimi measures. Arch. Rat. Mech. Analysis, 181, 401-448, 2006.
-
(2006)
Arch. Rat. Mech. Analysis
, vol.181
, pp. 401-448
-
-
Mielke, A.1
-
47
-
-
0346483176
-
Traveling waves in lattice dynamical systems
-
A. A. Pankov and K. Pflüger. Traveling waves in lattice dynamical systems. Math. Meth. Appl. Sci., 23, 1223-1235, 2000.
-
(2000)
Math. Meth. Appl. Sci.
, vol.23
, pp. 1223-1235
-
-
Pankov, A.A.1
Pflüger, K.2
-
48
-
-
0001648070
-
Convergence of solutions to nonlinear dispersive equations
-
M. Schonbek. Convergence of solutions to nonlinear dispersive equations. Comm. Part. Diff. Equa., 7, 959-1000, 1982.
-
(1982)
Comm. Part. Diff. Equa.
, vol.7
, pp. 959-1000
-
-
Schonbek, M.1
-
49
-
-
0007015954
-
Justification of modulation equations for hyperbolic systems via normal forms
-
G. Schneider. Justification of modulation equations for hyperbolic systems via normal forms. NoDEA Nonlinear Differential Equations Appl., 5(1), 69-82, 1998.
-
(1998)
NoDEA Nonlinear Differential Equations Appl.
, vol.5
, Issue.1
, pp. 69-82
-
-
Schneider, G.1
-
51
-
-
0001259642
-
Counter-propagating waves on fluid surfaces and the continuum limit for the Fermi-Pasta-Ulam model
-
K. Gröger, B. Fiedler, and J. Sprekels, editors, World Scientific
-
G. Schneider and C. E. Wayne. Counter-propagating waves on fluid surfaces and the continuum limit for the Fermi-Pasta-Ulam model. In K. Gröger, B. Fiedler, and J. Sprekels, editors, International Conference on Differential Equations, pages 390-403. World Scientific, 2000.
-
(2000)
International Conference on Differential Equations
, pp. 390-403
-
-
Schneider, G.1
Wayne, C.E.2
-
52
-
-
0030621830
-
A family of symplectic integrators: Stability, accuracy, and molecular dynamics Applications
-
R. D. Skeel, G. Yang, and T. Schlick. A family of symplectic integrators: Stability, accuracy, and molecular dynamics Applications. SIAM J. Sci. Comput., 18, 203-222, 1997.
-
(1997)
SIAM J. Sci. Comput.
, vol.18
, pp. 203-222
-
-
Skeel, R.D.1
Yang, G.2
Schlick, T.3
-
54
-
-
0000544179
-
Waves in nonlinear lattices
-
M. Toda. Waves in nonlinear lattices. Prog. Theor. Phys., 45, 174-200, 1970.
-
(1970)
Prog. Theor. Phys.
, vol.45
, pp. 174-200
-
-
Toda, M.1
-
56
-
-
84990557809
-
The Toda shock problem
-
S. Venakides, P. Deift, and R. Oba. The Toda shock problem. Comm. Pure Appl. Math., 44, 1171-1242, 1991.
-
(1991)
Comm. Pure Appl. Math.
, vol.44
, pp. 1171-1242
-
-
Venakides, S.1
Deift, P.2
Oba, R.3
-
57
-
-
84990614472
-
The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation
-
S. Venakides. The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation. Comm. Pure Appl. Math., 38, 883-909, 1985.
-
(1985)
Comm. Pure Appl. Math.
, vol.38
, pp. 883-909
-
-
Venakides, S.1
-
58
-
-
0000034625
-
Homoclinic period blow-up in reversible and conservative systems
-
A. Vanderbauwhede and B. Fiedler. Homoclinic period blow-up in reversible and conservative systems. Z. Angew. Math. Phys., 43, 292-318, 1992.
-
(1992)
Z. Angew. Math. Phys.
, vol.43
, pp. 292-318
-
-
Vanderbauwhede, A.1
Fiedler, B.2
|