메뉴 건너뛰기




Volumn 33, Issue 3, 2005, Pages 1078-1110

Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise

Author keywords

Blow up; Nonlinear Schr dinger equations; Stochastic partial differential equations; Support theorem; Variance identity; White noise

Indexed keywords


EID: 18844383396     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000964     Document Type: Article
Times cited : (96)

References (22)
  • 1
    • 0001635432 scopus 로고
    • Temperature effects in a nonlinear model of monolayer Scheibe aggregates
    • BANG, O., CHRISTIANSEN, P. L., IF, F., RASMUSSEN, K. O. and GAIDIDEI, Y. B. (1994). Temperature effects in a nonlinear model of monolayer Scheibe aggregates. Phys. Rev. E 49 4627-4636.
    • (1994) Phys. Rev. e , vol.49 , pp. 4627-4636
    • Bang, O.1    Christiansen, P.L.2    If, F.3    Rasmussen, K.O.4    Gaididei, Y.B.5
  • 3
    • 0000297769 scopus 로고    scopus 로고
    • On stochastic convolution in Banach spaces, and applications
    • BRZEZNIAK, Z. (1997). On stochastic convolution in Banach spaces, and applications. Stochastics Stochastics Rep. 61 245-295.
    • (1997) Stochastics Stochastics Rep. , vol.61 , pp. 245-295
    • Brzezniak, Z.1
  • 4
    • 0039833684 scopus 로고    scopus 로고
    • Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
    • BRZEZNIAK, Z. and PESZAT, S. (1999). Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process. Studio Math. 137 261-299.
    • (1999) Studio Math. , vol.137 , pp. 261-299
    • Brzezniak, Z.1    Peszat, S.2
  • 5
    • 0141973496 scopus 로고
    • Textos de Métodos Matématicos 26, Instituto de Matématica-UFRJ Rio de Janeiro, Brazil
    • CAZENAVE, T. (1993). An Introduction to Nonlinear Schrödinger Equations. Textos de Métodos Matématicos 26, Instituto de Matématica-UFRJ Rio de Janeiro, Brazil.
    • (1993) An Introduction to Nonlinear Schrödinger Equations
    • Cazenave, T.1
  • 7
    • 0033175771 scopus 로고    scopus 로고
    • A stochastic nonlinear Schrödinger equation with multiplicative noise
    • DE BOUARD, A. and DEBUSSCHE, A. (1999). A stochastic nonlinear Schrödinger equation with multiplicative noise. Comm. Math. Phys. 205 161-181.
    • (1999) Comm. Math. Phys. , vol.205 , pp. 161-181
    • De Bouard, A.1    Debussche, A.2
  • 8
    • 0036016202 scopus 로고    scopus 로고
    • On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation
    • DE BOUARD, A. and DEBUSSCHE, A. (2002). On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Probab. Theory Related Fields 123 76-96.
    • (2002) Probab. Theory Related Fields , vol.123 , pp. 76-96
    • De Bouard, A.1    Debussche, A.2
  • 9
    • 18844430466 scopus 로고    scopus 로고
    • Finite time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: The real noise case
    • DE BOUARD, A. and DEBUSSCHE, A. (2002). Finite time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: The real noise case. Contemp. Math. 301 183-194.
    • (2002) Contemp. Math. , vol.301 , pp. 183-194
    • De Bouard, A.1    Debussche, A.2
  • 11
    • 1542718372 scopus 로고    scopus 로고
    • A semi-discrete scheme for the stochastic nonlinear Schrödinger equation
    • DE BOUARD, A. and DEBUSSCHE, A. (2004). A semi-discrete scheme for the stochastic nonlinear Schrödinger equation. Numer. Math. 96 733-770.
    • (2004) Numer. Math. , vol.96 , pp. 733-770
    • De Bouard, A.1    Debussche, A.2
  • 12
    • 0037084451 scopus 로고    scopus 로고
    • Numerical simulation of focusing stochastic nonlinear Schrödinger equations
    • DEBUSSCHE, A. and DI MENZA, L. (2002). Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Phys. D 162 131-154.
    • (2002) Phys. D , vol.162 , pp. 131-154
    • Debussche, A.1    Di Menza, L.2
  • 14
    • 0032302719 scopus 로고    scopus 로고
    • Asymptotic transmission of solitons through random media
    • GARNIER, J. (1998). Asymptotic transmission of solitons through random media. SIAM J. Appl. Math. 58 1969-1995.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1969-1995
    • Garnier, J.1
  • 15
    • 36749114276 scopus 로고
    • On the blowing-up of solutions to the Cauchy problem for the nonlinear Schrödinger equation
    • GLASSEY, R. T. (1977). On the blowing-up of solutions to the Cauchy problem for the nonlinear Schrödinger equation. J. Math. Phys. 18 1794-1797.
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1
  • 16
    • 0040361064 scopus 로고    scopus 로고
    • Existence of strong solutions for It̂'s stochastic equations via approximations
    • GYÖNGY, I. and KRYLOV, N. V. (1996). Existence of strong solutions for It̂'s stochastic equations via approximations. Probab. Theory Related Fields 105 143-158.
    • (1996) Probab. Theory Related Fields , vol.105 , pp. 143-158
    • Gyöngy, I.1    Krylov, N.V.2
  • 21
    • 0001076665 scopus 로고
    • Dynamics of optical pulses in randomly birefrengent fibers
    • UEDA, T. and KATH, W. L. (1992). Dynamics of optical pulses in randomly birefrengent fibers. Phys. D 55 166-181.
    • (1992) Phys. D , vol.55 , pp. 166-181
    • Ueda, T.1    Kath, W.L.2
  • 22
    • 0001596227 scopus 로고
    • Collapse of Langmuir waves
    • ZAKHAROV, V. E. (1972). Collapse of Langmuir waves. Soviet Phys. JETP 35 908-914.
    • (1972) Soviet Phys. JETP , vol.35 , pp. 908-914
    • Zakharov, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.