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Volumn 238, Issue 9-10, 2009, Pages 860-879

Coupled mode equations and gap solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential

Author keywords

Bloch wave analysis; Coupled Mode Equations; Gap solitons; Gross Pitaevskii equation; Lyapunov Schmidt reduction; Periodic Nonlinear Schr dinger equation

Indexed keywords

BOSE-EINSTEIN CONDENSATION; SOLITONS; WAVE EFFECTS;

EID: 64249171838     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2009.02.013     Document Type: Article
Times cited : (32)

References (40)
  • 1
    • 0012593396 scopus 로고    scopus 로고
    • Nonlinear guided waves and spatial solitons in a periodic layered medium
    • Sukhorukov A.A., and Kivshar Y. Nonlinear guided waves and spatial solitons in a periodic layered medium. J. Opt. Soc. Am. B 19 (2002) 772-781
    • (2002) J. Opt. Soc. Am. B , vol.19 , pp. 772-781
    • Sukhorukov, A.A.1    Kivshar, Y.2
  • 4
    • 0035844507 scopus 로고    scopus 로고
    • Self-trapping and stable localized modes in nonlinear photonic crystals
    • Mingaleev S.F., and Kivshar Y.S. Self-trapping and stable localized modes in nonlinear photonic crystals. Phys. Rev. Lett. 86 (2001) 5474-5477
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 5474-5477
    • Mingaleev, S.F.1    Kivshar, Y.S.2
  • 6
    • 51249193203 scopus 로고
    • Structure of a quantized vortex in boson systems
    • [Hydrodynamics of a superfluid concentrate, J. Math. Phys. 4 (1963) 195-207]
    • Gross E.P. Structure of a quantized vortex in boson systems. Il Nuovo Cimiento 20 (1961) 454 [Hydrodynamics of a superfluid concentrate, J. Math. Phys. 4 (1963) 195-207]
    • (1961) Il Nuovo Cimiento , vol.20 , pp. 454
    • Gross, E.P.1
  • 7
    • 0000189868 scopus 로고
    • Vortex lines in an imperfect Bose gas
    • Pitaevskii L.P. Vortex lines in an imperfect Bose gas. Zh. Eksp. Teor. Fiz. 40 (1961) 646-651
    • (1961) Zh. Eksp. Teor. Fiz. , vol.40 , pp. 646-651
    • Pitaevskii, L.P.1
  • 8
    • 0000196586 scopus 로고
    • Vortex lines in an imperfect Bose gas
    • Pitaevskii L.P. Vortex lines in an imperfect Bose gas. Sov. Phys. JETP 13 (1961) 451-454
    • (1961) Sov. Phys. JETP , vol.13 , pp. 451-454
    • Pitaevskii, L.P.1
  • 9
    • 0038541592 scopus 로고    scopus 로고
    • Matter-wave gap solitons in atomic band-gap structures
    • Ostrovskaya E.A., and Kivshar Yu.S. Matter-wave gap solitons in atomic band-gap structures. Phys. Rev. Lett. 90 (2003) 160407
    • (2003) Phys. Rev. Lett. , vol.90 , pp. 160407
    • Ostrovskaya, E.A.1    Kivshar, Yu.S.2
  • 10
    • 33646983153 scopus 로고    scopus 로고
    • Optical solitary waves in two and three dimensional photonic bandgap structures
    • Aközbek N., and John S. Optical solitary waves in two and three dimensional photonic bandgap structures. Phys. Rev. E 57 (1998) 2287-2319
    • (1998) Phys. Rev. E , vol.57 , pp. 2287-2319
    • Aközbek, N.1    John, S.2
  • 11
    • 0037434990 scopus 로고    scopus 로고
    • Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices
    • Fleischer J.W., Segev M., Efremidis N.K., and Christodoulides D.N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422 (2003) 147
    • (2003) Nature , vol.422 , pp. 147
    • Fleischer, J.W.1    Segev, M.2    Efremidis, N.K.3    Christodoulides, D.N.4
  • 12
    • 22544487243 scopus 로고    scopus 로고
    • Optical soliton bullets in (2 + 1) D nonlinear Bragg resonant periodic geometries
    • Dohnal T., and Aceves A.B. Optical soliton bullets in (2 + 1) D nonlinear Bragg resonant periodic geometries. Stud. Appl. Math. 115 (2005) 209-232
    • (2005) Stud. Appl. Math. , vol.115 , pp. 209-232
    • Dohnal, T.1    Aceves, A.B.2
  • 13
    • 0041639619 scopus 로고    scopus 로고
    • Multidimensional solitons in periodic potentials
    • Baizakov B.B., Malomed B.A., and Salerno M. Multidimensional solitons in periodic potentials. Europhys. Lett. 63 (2003) 642-648
    • (2003) Europhys. Lett. , vol.63 , pp. 642-648
    • Baizakov, B.B.1    Malomed, B.A.2    Salerno, M.3
  • 14
    • 21844500101 scopus 로고
    • Two-dimensional gap solitons in a nonlinear periodic slab waveguide
    • Aceves A.B., Costantini B., and De Angelis C. Two-dimensional gap solitons in a nonlinear periodic slab waveguide. J. Opt. Soc. Am. B 12 (1995) 1475-1479
    • (1995) J. Opt. Soc. Am. B , vol.12 , pp. 1475-1479
    • Aceves, A.B.1    Costantini, B.2    De Angelis, C.3
  • 15
    • 0037143214 scopus 로고    scopus 로고
    • Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses
    • Sipe J.E., De Sterke C.M., and Eggleton B.J. Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses. J. Mod. Opt. 49 (2002) 1437-1452
    • (2002) J. Mod. Opt. , vol.49 , pp. 1437-1452
    • Sipe, J.E.1    De Sterke, C.M.2    Eggleton, B.J.3
  • 16
    • 1042277258 scopus 로고    scopus 로고
    • Gap-soliton bullets in waveguide gratings
    • Aceves A.B., Fibich G., and Ilan B. Gap-soliton bullets in waveguide gratings. Physica D 189 (2004) 277-286
    • (2004) Physica D , vol.189 , pp. 277-286
    • Aceves, A.B.1    Fibich, G.2    Ilan, B.3
  • 17
    • 25144501646 scopus 로고    scopus 로고
    • Modeling of wave resonances in low-contrast photonic crystals
    • Agueev D., and Pelinovsky D. Modeling of wave resonances in low-contrast photonic crystals. SIAM J. Appl. Math. 65 (2005) 1101-1129
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 1101-1129
    • Agueev, D.1    Pelinovsky, D.2
  • 18
    • 0000764814 scopus 로고    scopus 로고
    • Coupled-mode theory for light propagation through deep nonlinear gratings
    • de Sterke C.M., Salinas D.G., and Sipe J.E. Coupled-mode theory for light propagation through deep nonlinear gratings. Phys. Rev. E 54 (1996) 1969-1989
    • (1996) Phys. Rev. E , vol.54 , pp. 1969-1989
    • de Sterke, C.M.1    Salinas, D.G.2    Sipe, J.E.3
  • 19
    • 34248203162 scopus 로고    scopus 로고
    • Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media
    • Shi Z., and Yang J. Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media. Phys. Rev. E 75 (2007) 056602
    • (2007) Phys. Rev. E , vol.75 , pp. 056602
    • Shi, Z.1    Yang, J.2
  • 20
    • 84867925558 scopus 로고    scopus 로고
    • Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
    • Dohnal T., Pelinovsky D., and Schneider G. Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential. J. Nonlinear Sci. 19 (2009) 95-131
    • (2009) J. Nonlinear Sci. , vol.19 , pp. 95-131
    • Dohnal, T.1    Pelinovsky, D.2    Schneider, G.3
  • 21
    • 21344495382 scopus 로고
    • Nonpersistence of breather families for the perturbed sine Gordon equation
    • Denzler J. Nonpersistence of breather families for the perturbed sine Gordon equation. Comm. Math. Phys. 158 2 (1993) 397-430
    • (1993) Comm. Math. Phys. , vol.158 , Issue.2 , pp. 397-430
    • Denzler, J.1
  • 23
    • 27844448598 scopus 로고    scopus 로고
    • Periodic nonlinear Schrödinger equation with application to photonic crystals
    • Pankov A. Periodic nonlinear Schrödinger equation with application to photonic crystals. Milan J. Math. 73 (2005) 259-287
    • (2005) Milan J. Math. , vol.73 , pp. 259-287
    • Pankov, A.1
  • 24
    • 52449105521 scopus 로고    scopus 로고
    • Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
    • Pelinovsky D., and Schneider G. Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Appl. Anal. 86 (2007) 1017-1036
    • (2007) Appl. Anal. , vol.86 , pp. 1017-1036
    • Pelinovsky, D.1    Schneider, G.2
  • 26
    • 0035504546 scopus 로고    scopus 로고
    • Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems
    • Schneider G., and Uecker H. Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymp. Anal. 28 (2001) 163-180
    • (2001) Asymp. Anal. , vol.28 , pp. 163-180
    • Schneider, G.1    Uecker, H.2
  • 27
    • 33750451942 scopus 로고    scopus 로고
    • Justification of the nonlinear Schrödinger equation in spatially periodic media
    • Busch K., Schneider G., Tkeshelashvili L., and Uecker H. Justification of the nonlinear Schrödinger equation in spatially periodic media. Z. Angew. Math. Phys. 57 (2006) 905-939
    • (2006) Z. Angew. Math. Phys. , vol.57 , pp. 905-939
    • Busch, K.1    Schneider, G.2    Tkeshelashvili, L.3    Uecker, H.4
  • 29
    • 34250781014 scopus 로고    scopus 로고
    • On occurrence of spectral edges for periodic operators inside the Brillouin zone
    • Harrison J.M., Kuchment P., Sobolev A., and Winn B. On occurrence of spectral edges for periodic operators inside the Brillouin zone. J. Phys. A: Math. Theor. 40 (2007) 7597-7618
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 7597-7618
    • Harrison, J.M.1    Kuchment, P.2    Sobolev, A.3    Winn, B.4
  • 31
    • 37649031143 scopus 로고    scopus 로고
    • Bifurcations and stability of gap solitons in periodic structures
    • Pelinovsky D.E., Sukhorukov A.A., and Kivshar Y. Bifurcations and stability of gap solitons in periodic structures. Phys. Rev. E 70 (2004) 036618
    • (2004) Phys. Rev. E , vol.70 , pp. 036618
    • Pelinovsky, D.E.1    Sukhorukov, A.A.2    Kivshar, Y.3
  • 34
    • 51249187120 scopus 로고
    • Theory of Bloch waves
    • Wilcox C.H. Theory of Bloch waves. J. Analyse Math. 33 (1978) 146-167
    • (1978) J. Analyse Math. , vol.33 , pp. 146-167
    • Wilcox, C.H.1
  • 39
    • 34347337418 scopus 로고    scopus 로고
    • Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
    • Abdullaev F., Abdumalikov A., and Galimzyanov R. Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices. Phys. Lett. A 367 (2007) 149-155
    • (2007) Phys. Lett. A , vol.367 , pp. 149-155
    • Abdullaev, F.1    Abdumalikov, A.2    Galimzyanov, R.3
  • 40
    • 0000747159 scopus 로고    scopus 로고
    • Nonlinear propagation of light in one-dimensional periodic structures
    • Goodman R.H., Weinstein M.I., and Holmes P.J. Nonlinear propagation of light in one-dimensional periodic structures. J. Nonlinear Sci. 11 (2001) 123-168
    • (2001) J. Nonlinear Sci. , vol.11 , pp. 123-168
    • Goodman, R.H.1    Weinstein, M.I.2    Holmes, P.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.