| Title:
|
Cauchy problem for multidimensional coupled system of nonlinear Schrödinger equation and generalized IMBq equation (English) |
| Author:
|
Guowang, Chen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
15-38 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
coupled system of nonlinear Schrödinger equation and generalized IMBq |
| Keyword:
|
multidimensional |
| Keyword:
|
periodic boundary value problem |
| Keyword:
|
Cauchy problem |
| Keyword:
|
generalized local solution |
| Keyword:
|
classical local solution |
| MSC:
|
35D05 |
| MSC:
|
35K55 |
| MSC:
|
35L35 |
| MSC:
|
35Q55 |
| idZBL:
|
Zbl 0940.35181 |
| idMR:
|
MR1622316 |
| . |
| Date available:
|
2009-01-08T18:38:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118981 |
| . |
| Reference:
|
[1] Makhankov V.G.: On stationary solutions of the Schrödinger equation with a self-consistent potential satisfying Boussinesq's equations.Phys. Lett. 50 A (1974), 42-44. |
| Reference:
|
[2] Makhankov V.G.: Dynamics of classical solitons (in non-integrable systems).Physics Reports, A review section of Physics Letters (section C), \bf 35(1) (1978), 1-128. MR 0481361 |
| Reference:
|
[3] Nishikawa K., Hajo H., Mima K., Ikezi H.: Coupled nonlinear electron-plasma and ion- acoustic waves.Phys. Rev. Lett. 33 (1974), 148-150. |
| Reference:
|
[4] Makhankov V.G.: Preprint.JINR E5-8359, Dubna, 1974. |
| Reference:
|
[5] Bogoluosksy J.L., Makhankov V.G.: Preprint.JINR E4-9425, Dubna, 1975. |
| Reference:
|
[6] Reed M., Simon B.: Method of Modern Mathematical Physics.Academic Press, New York and London, 1972. MR 0493419 |
| Reference:
|
[7] Vejvoda O.: Partial Differential Equations: Time-Periodic Solutions.Martinus Nijhoff Publishers, The Hague, Boston, London, 1982. Zbl 0501.35001 |
| Reference:
|
[8] Maz'ja V.G.: Sobolev Spaces.Springer-Verlag, 1985. Zbl 0692.46023, MR 0817985 |
| Reference:
|
[9] Friedman A.: Partial Differential Equations of Parabolic Type.Prentice-Hall, Inc., 1964. Zbl 0173.12701, MR 0181836 |
| Reference:
|
[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. Zbl 0822.35094 |
| Reference:
|
[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. MR 0901636 |
| Reference:
|
[12] Yosida K.: Functional Analysis.Springer, 1978. Zbl 0830.46001, MR 0500055 |
| . |
