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Stability of interacting traveling waves in reaction-convection-diffusion systems
Interaction of oscillatory packets of water waves
1. | Mathematical Institute, University of Leiden, 2300 RA Leiden, Netherlands |
2. | Institut für Analysis, Dynamik und Modellierung, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart |
References:
[1] |
A. Babin and A. Figotin., Linear superposition in nonlinear wave dynamics., Rev. Math. Phys., 18 (2006), 971. Google Scholar |
[2] |
M. Chirilus-Bruckner, G. Schneider and H. Uecker., On the interaction of NLS-described modulating pulses with different carrier waves., Math. Methods Appl. Sci., 30 (2007), 1965. Google Scholar |
[3] |
M. Chirilus-Bruckner, C. Chong, G. Schneider and H. Uecker., Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves., J. Math. Anal. Appl., 347 (2008), 304. Google Scholar |
[4] |
M. Chirilus-Bruckner and G. Schneider., Detection of standing pulses in periodic media by pulse interaction., J. Differential Equations, 253 (2012), 2161. Google Scholar |
[5] |
W.P. Düll, G. Schneider and C.E. Wayne., Justification of the nonlinear schrödinger equation for the evolution of gravity driven 2d surface water waves in a canal of finite depth., Archive for Rational Mechanics and Analysis, (2015). Google Scholar |
[6] |
M. Oikawa and N. Yajima., A perturbation approach to nonlinear systems. ii. interaction of nonlinear modulated waves., Journal of the Physical Society of Japan, 37 (1974), 486. Google Scholar |
[7] |
R.D. Pierce and C.E. Wayne., On the validity of mean-field amplitude equations for counterpropagating wavetrains., Nonlinearity, 8 (1995), 769. Google Scholar |
[8] |
G. Schneider, H. Uecker and M. Wand., Interaction of modulated pulses in nonlinear oscillator chains., Journal of Difference Eq. and Appl., 17 (2011), 279. Google Scholar |
[9] |
L. Tkeshelashvili, S. Pereira and K. Busch., General theory of nonresonant wave interaction: Giant soliton shift in photonic band gap materials., Europhysics Letters, 68 (2004). Google Scholar |
[10] |
N. Totz and S. Wu., A rigorous justification of the modulation approximation to the 2D full water wave problem., Commun. Math. Phys., 310 (2012), 817. Google Scholar |
[11] |
V.E. Zakharov., Stability of periodic waves of finite amplitude on the surface of a deep fluid., Sov. Phys. J. Appl. Mech. Tech. Phys, 4 (1968), 190. Google Scholar |
show all references
References:
[1] |
A. Babin and A. Figotin., Linear superposition in nonlinear wave dynamics., Rev. Math. Phys., 18 (2006), 971. Google Scholar |
[2] |
M. Chirilus-Bruckner, G. Schneider and H. Uecker., On the interaction of NLS-described modulating pulses with different carrier waves., Math. Methods Appl. Sci., 30 (2007), 1965. Google Scholar |
[3] |
M. Chirilus-Bruckner, C. Chong, G. Schneider and H. Uecker., Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves., J. Math. Anal. Appl., 347 (2008), 304. Google Scholar |
[4] |
M. Chirilus-Bruckner and G. Schneider., Detection of standing pulses in periodic media by pulse interaction., J. Differential Equations, 253 (2012), 2161. Google Scholar |
[5] |
W.P. Düll, G. Schneider and C.E. Wayne., Justification of the nonlinear schrödinger equation for the evolution of gravity driven 2d surface water waves in a canal of finite depth., Archive for Rational Mechanics and Analysis, (2015). Google Scholar |
[6] |
M. Oikawa and N. Yajima., A perturbation approach to nonlinear systems. ii. interaction of nonlinear modulated waves., Journal of the Physical Society of Japan, 37 (1974), 486. Google Scholar |
[7] |
R.D. Pierce and C.E. Wayne., On the validity of mean-field amplitude equations for counterpropagating wavetrains., Nonlinearity, 8 (1995), 769. Google Scholar |
[8] |
G. Schneider, H. Uecker and M. Wand., Interaction of modulated pulses in nonlinear oscillator chains., Journal of Difference Eq. and Appl., 17 (2011), 279. Google Scholar |
[9] |
L. Tkeshelashvili, S. Pereira and K. Busch., General theory of nonresonant wave interaction: Giant soliton shift in photonic band gap materials., Europhysics Letters, 68 (2004). Google Scholar |
[10] |
N. Totz and S. Wu., A rigorous justification of the modulation approximation to the 2D full water wave problem., Commun. Math. Phys., 310 (2012), 817. Google Scholar |
[11] |
V.E. Zakharov., Stability of periodic waves of finite amplitude on the surface of a deep fluid., Sov. Phys. J. Appl. Mech. Tech. Phys, 4 (1968), 190. Google Scholar |
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