Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation

Chen Guowang

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 15-38
  • ISSN: 0010-2628

Abstract

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The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation i ε t + ∇ 2 ε - u ε = 0 , u t t - ∇ 2 u - a ∇ 2 u t t = ∇ 2 f ( u ) + ∇ 2 ( | ε | 2 ) are proved.

How to cite

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Guowang, Chen. "Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 15-38. <http://eudml.org/doc/248275>.

@article{Guowang1998,
abstract = {The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation \[ i\varepsilon \_t+\nabla ^2\varepsilon -u\varepsilon =0, \]\[ u\_\{tt\}-\nabla ^2u-a\nabla ^2u\_\{tt\}=\nabla ^2f(u)+\nabla ^2(|\varepsilon |^2) \] are proved.},
author = {Guowang, Chen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution; periodic boundary value problem; generalized local solution; classical local solution},
language = {eng},
number = {1},
pages = {15-38},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation},
url = {http://eudml.org/doc/248275},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Guowang, Chen
TI - Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 15
EP - 38
AB - The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation \[ i\varepsilon _t+\nabla ^2\varepsilon -u\varepsilon =0, \]\[ u_{tt}-\nabla ^2u-a\nabla ^2u_{tt}=\nabla ^2f(u)+\nabla ^2(|\varepsilon |^2) \] are proved.
LA - eng
KW - coupled system of nonlinear Schrödinger equation and generalized IMBq; multidimensional; periodic boundary value problem; Cauchy problem; generalized local solution; classical local solution; periodic boundary value problem; generalized local solution; classical local solution
UR - http://eudml.org/doc/248275
ER -

References

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  2. Makhankov V.G., Dynamics of classical solitons (in non-integrable systems), Physics Reports, A review section of Physics Letters (section C), MR0481361
  3. Nishikawa K., Hajo H., Mima K., Ikezi H., Coupled nonlinear electron-plasma and ion- acoustic waves, Phys. Rev. Lett. 33 (1974), 148-150. (1974) 
  4. Makhankov V.G., Preprint, JINR E5-8359, Dubna, 1974. 
  5. Bogoluosksy J.L., Makhankov V.G., Preprint, JINR E4-9425, Dubna, 1975. 
  6. Reed M., Simon B., Method of Modern Mathematical Physics, Academic Press, New York and London, 1972. MR0493419
  7. Vejvoda O., Partial Differential Equations: Time-Periodic Solutions, Martinus Nijhoff Publishers, The Hague, Boston, London, 1982. Zbl0501.35001
  8. Maz'ja V.G., Sobolev Spaces, Springer-Verlag, 1985. Zbl0692.46023MR0817985
  9. Friedman A., Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., 1964. Zbl0173.12701MR0181836
  10. Chen Guowang, Yang Zhijian, Zhao Zhancai, Initial value problems and first boundary problems for a class of quasilinear wave equations, Acta Mathematicae Applicatae Sinica 9 (1993), 289-301. (1993) Zbl0822.35094
  11. Sun Hesheng, On the mixed initial boundary value problem for semilinear degenerate evolution equation (in Chinese), Chinese Annals of Mathematics 8 (A) (1987), 32-43. (1987) MR0901636
  12. Yosida K., Functional Analysis, Springer, 1978. Zbl0830.46001MR0500055

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