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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 8
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Original Articles

Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Dmitry Pelinovsky Institut für Analysis, Dynamik und Modellierung Fakultät für Mathematik und Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanyCorrespondence[email protected]
&
Guido Schneider Institut für Analysis, Dynamik und Modellierung Fakultät für Mathematik und Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Pages 1017-1036 | Received 08 Feb 2007, Accepted 04 Jun 2007, Published online: 24 Sep 2007

Citations (23)

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Tomáš Dohnal & Daniel Rudolf. (2020) NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝd. Applicable Analysis 99:10, pages 1685-1723.
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Articles from other publishers (22)

Tomáš Dohnal & Lisa Wahlers. (2021) Bifurcation of Gap Solitons in Coupled Mode Equations in d Dimensions. Journal of Dynamics and Differential Equations 34:3, pages 2105-2122.
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Adilbek Kairzhan, Diego Noja & Dmitry E Pelinovsky. (2022) Standing waves on quantum graphs. Journal of Physics A: Mathematical and Theoretical 55:24, pages 243001.
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B. Buffoni, M. D. Groves & E. Wahlén. (2022) Fully Localised Three-Dimensional Gravity-Capillary Solitary Waves on Water of Infinite Depth. Journal of Mathematical Fluid Mechanics 24:2.
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Tomáš Dohnal & Dmitry Pelinovsky. (2019) Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with 𝒫𝒯-symmetry. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150:1, pages 171-204.
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Jack Arbunich & Christof Sparber. (2018) Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures. Journal of Mathematical Physics 59:1.
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Steffen Gilg, Dmitry Pelinovsky & Guido Schneider. (2016) Validity of the NLS approximation for periodic quantum graphs. Nonlinear Differential Equations and Applications NoDEA 23:6.
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Eric Dumas & Dmitry Pelinovsky. (2014) Justification of the log--KdV Equation in Granular Chains: The Case of Precompression. SIAM Journal on Mathematical Analysis 46:6, pages 4075-4103.
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Tomáš Dohnal. (2014) Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials. SIAM Journal on Applied Mathematics 74:2, pages 306-321.
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Tomáš Dohnal & Willy Dörfler. (2013) Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals. Multiscale Modeling & Simulation 11:1, pages 162-191.
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R. Marangell, H. Susanto & C.K.R.T. Jones. (2012) Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations. Journal of Differential Equations 253:4, pages 1191-1205.
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Boris A. Malomed, Thomas Wagenknecht & Kazuyuki Yagasaki. (2012) Families of solitons in Bragg supergratings. Physica D: Nonlinear Phenomena 241:11, pages 1043-1058.
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Dmitry E. Pelinovsky, Gideon Simpson & Michael I. Weinstein. (2012) Polychromatic Solitary Waves in a Periodic and Nonlinear Maxwell System. SIAM Journal on Applied Dynamical Systems 11:1, pages 478-506.
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G. Simpson & M. I. Weinstein. (2011) Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations. Multiscale Modeling & Simulation 9:3, pages 955-990.
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Carsten Blank, Martina Chirilus-Bruckner, Vincent Lescarret & Guido Schneider. (2011) Breather Solutions in Periodic Media. Communications in Mathematical Physics 302:3, pages 815-841.
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M. A. Hoefer & M. I. Weinstein. (2011) Defect Modes and Homogenization of Periodic Schrödinger Operators. SIAM Journal on Mathematical Analysis 43:2, pages 971-996.
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B. Ilan & M. I. Weinstein. (2010) Band-Edge Solitons, Nonlinear Schrödinger/Gross–Pitaevskii Equations, and Effective Media. Multiscale Modeling & Simulation 8:4, pages 1055-1101.
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Tomáš Dohnal & Hannes Uecker. (2009) Coupled mode equations and gap solitons for the 2D Gross–Pitaevskii equation with a non-separable periodic potential. Physica D: Nonlinear Phenomena 238:9-10, pages 860-879.
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Tomáš Dohnal, Dmitry Pelinovsky & Guido Schneider. (2008) Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential. Journal of Nonlinear Science 19:2, pages 95-131.
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Mathieu Colin & David Lannes. (2009) Short Pulses Approximations in Dispersive Media. SIAM Journal on Mathematical Analysis 41:2, pages 708-732.
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Dmitry Pelinovsky, Guido Schneider & Robert S. MacKay. (2008) Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential. Communications in Mathematical Physics 284:3, pages 803-831.
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Dmitry Pelinovsky & Guido Schneider. (2008) Moving gap solitons in periodic potentials. Mathematical Methods in the Applied Sciences 31:14, pages 1739-1760.
Crossref
Johannes Giannoulis, Alexander Mielke & Christof Sparber. (2008) Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential. Journal of Differential Equations 245:4, pages 939-963.
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