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A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations
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The three-dimensional center problem for the zero-Hopf singularity
KdV waves in atomic chains with nonlocal interactions
1. | Westfälische Wilhelms-Universität Münster, Institut für Numerische und Angewandte Mathematik, Einsteinstraße 62, 48149 Münster, Germany |
2. | Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, 85747 Garching, Germany |
References:
[1] |
M. Chirilus-Bruckner, C. Chong, O. Prill and G. Schneider, Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations,, Discrete Contin. Dyn. Syst. Ser. S, 5 (2012), 879.
doi: 10.3934/dcdss.2012.5.879. |
[2] |
G. Friesecke and A. Mikikits-Leitner, Cnoidal waves on Fermi-Pasta-Ulam lattices, 2014,, To appear in J. Dyn. Diff. Equat., (). Google Scholar |
[3] |
G. Friesecke and R. L. Pego, Solitary waves on FPU lattices. I. Qualitative properties, renormalization and continuum limit,, Nonlinearity, 12 (1999), 1601.
doi: 10.1088/0951-7715/12/6/311. |
[4] |
G. Friesecke and R. L. Pego, Solitary waves on FPU lattices. II. Linear implies nonlinear stability,, Nonlinearity, 15 (2002), 1343.
doi: 10.1088/0951-7715/15/4/317. |
[5] |
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices. III. Howland-type Floquet theory,, Nonlinearity, 17 (2004), 207.
doi: 10.1088/0951-7715/17/1/013. |
[6] |
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices. IV. Proof of stability at low energy,, Nonlinearity, 17 (2004), 229.
doi: 10.1088/0951-7715/17/1/014. |
[7] |
J. Gaison, S. Moskow, J. D. Wright and Q. Zhang, Approximation of polyatomic FPU lattices by KdV equations,, Multiscale Model. Simul., 12 (2014), 953.
doi: 10.1137/130941638. |
[8] |
M. Herrmann, Unimodal wavetrains and solitons in convex Fermi-Pasta-Ulam chains,, Proc. Roy. Soc. Edinburgh Sect. A, 140 (2010), 753.
doi: 10.1017/S0308210509000146. |
[9] |
M. Herrmann, K. Matthies, H. Schwetlick and J. Zimmer, Subsonic phase transition waves in bistable lattice models with small spinodal region,, SIAM J. Math. Anal., 45 (2013), 2625.
doi: 10.1137/120877878. |
[10] |
M. Herrmann and J. D. M. Rademacher, Heteroclinic travelling waves in convex FPU-type chains,, SIAM J. Math. Anal., 42 (2010), 1483.
doi: 10.1137/080743147. |
[11] |
A. Hoffman and C. E. Wayne, Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice,, Nonlinearity, 21 (2008), 2911.
doi: 10.1088/0951-7715/21/12/011. |
[12] |
A. Hoffman and C. E. Wayne, Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model,, J. Dynam. Differential Equations, 21 (2009), 343.
doi: 10.1007/s10884-009-9134-9. |
[13] |
A. Hoffman and C. E. Wayne, A simple proof of the stability of solitary waves in the Fermi-Pasta-Ulam model near the KdV limit,, in Infinite dimensional dynamical systems, (2013), 185.
doi: 10.1007/978-1-4614-4523-4_7. |
[14] |
T. Mizumachi, $N$-soliton states of the Fermi-Pasta-Ulam lattices,, SIAM J. Math. Anal., 43 (2011), 2170.
doi: 10.1137/100792457. |
[15] |
T. Mizumachi, Asymptotic stability of $N$-solitary waves of the FPU lattices,, Arch. Ration. Mech. Anal., 207 (2013), 393.
doi: 10.1007/s00205-012-0564-x. |
[16] |
P. M. Morse and H. Feshbach, Methods of Theoretical Physics. 2 volumes,, McGraw-Hill Book Co., (1953).
|
[17] |
G. Schneider and C. E. Wayne, Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model,, in International Conference on Differential Equations, (1999), 390.
|
[18] |
N. J. Zabusky and M. D. Kruskal, Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states,, Phys. Rev. Lett., 15 (1965), 240.
doi: 10.1103/PhysRevLett.15.240. |
show all references
References:
[1] |
M. Chirilus-Bruckner, C. Chong, O. Prill and G. Schneider, Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations,, Discrete Contin. Dyn. Syst. Ser. S, 5 (2012), 879.
doi: 10.3934/dcdss.2012.5.879. |
[2] |
G. Friesecke and A. Mikikits-Leitner, Cnoidal waves on Fermi-Pasta-Ulam lattices, 2014,, To appear in J. Dyn. Diff. Equat., (). Google Scholar |
[3] |
G. Friesecke and R. L. Pego, Solitary waves on FPU lattices. I. Qualitative properties, renormalization and continuum limit,, Nonlinearity, 12 (1999), 1601.
doi: 10.1088/0951-7715/12/6/311. |
[4] |
G. Friesecke and R. L. Pego, Solitary waves on FPU lattices. II. Linear implies nonlinear stability,, Nonlinearity, 15 (2002), 1343.
doi: 10.1088/0951-7715/15/4/317. |
[5] |
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices. III. Howland-type Floquet theory,, Nonlinearity, 17 (2004), 207.
doi: 10.1088/0951-7715/17/1/013. |
[6] |
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices. IV. Proof of stability at low energy,, Nonlinearity, 17 (2004), 229.
doi: 10.1088/0951-7715/17/1/014. |
[7] |
J. Gaison, S. Moskow, J. D. Wright and Q. Zhang, Approximation of polyatomic FPU lattices by KdV equations,, Multiscale Model. Simul., 12 (2014), 953.
doi: 10.1137/130941638. |
[8] |
M. Herrmann, Unimodal wavetrains and solitons in convex Fermi-Pasta-Ulam chains,, Proc. Roy. Soc. Edinburgh Sect. A, 140 (2010), 753.
doi: 10.1017/S0308210509000146. |
[9] |
M. Herrmann, K. Matthies, H. Schwetlick and J. Zimmer, Subsonic phase transition waves in bistable lattice models with small spinodal region,, SIAM J. Math. Anal., 45 (2013), 2625.
doi: 10.1137/120877878. |
[10] |
M. Herrmann and J. D. M. Rademacher, Heteroclinic travelling waves in convex FPU-type chains,, SIAM J. Math. Anal., 42 (2010), 1483.
doi: 10.1137/080743147. |
[11] |
A. Hoffman and C. E. Wayne, Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice,, Nonlinearity, 21 (2008), 2911.
doi: 10.1088/0951-7715/21/12/011. |
[12] |
A. Hoffman and C. E. Wayne, Asymptotic two-soliton solutions in the Fermi-Pasta-Ulam model,, J. Dynam. Differential Equations, 21 (2009), 343.
doi: 10.1007/s10884-009-9134-9. |
[13] |
A. Hoffman and C. E. Wayne, A simple proof of the stability of solitary waves in the Fermi-Pasta-Ulam model near the KdV limit,, in Infinite dimensional dynamical systems, (2013), 185.
doi: 10.1007/978-1-4614-4523-4_7. |
[14] |
T. Mizumachi, $N$-soliton states of the Fermi-Pasta-Ulam lattices,, SIAM J. Math. Anal., 43 (2011), 2170.
doi: 10.1137/100792457. |
[15] |
T. Mizumachi, Asymptotic stability of $N$-solitary waves of the FPU lattices,, Arch. Ration. Mech. Anal., 207 (2013), 393.
doi: 10.1007/s00205-012-0564-x. |
[16] |
P. M. Morse and H. Feshbach, Methods of Theoretical Physics. 2 volumes,, McGraw-Hill Book Co., (1953).
|
[17] |
G. Schneider and C. E. Wayne, Counter-propagating waves on fluid surfaces and the continuum limit of the Fermi-Pasta-Ulam model,, in International Conference on Differential Equations, (1999), 390.
|
[18] |
N. J. Zabusky and M. D. Kruskal, Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states,, Phys. Rev. Lett., 15 (1965), 240.
doi: 10.1103/PhysRevLett.15.240. |
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