Solving (3+1)‐dimensional non‐linear Schrödinger equation by means of (3+1)‐dimensional Painlevé integrable model

作者: Hang-yu Ruan , Yi-xin Chen

DOI: 10.1002/MMA.258

关键词:

摘要: A conformal invariant asymptotic expansion approach is used to solve the (3+1)-dimensional non-linear Schrodinger (NLS) equation. Some new integrable models under condition that they are and possess Painleve property obtained. These can be NLS equation approximately. In some special cases, approximate solutions become exact.

参考文章(16)
Roger G. Newton, Erratum: Inverse scattering. II. Three dimensions [J. Math. Phys. 21, 1698 (1980)] Journal of Mathematical Physics. ,vol. 22, pp. 631- 631 ,(1981) , 10.1063/1.524916
Gu Chaohao, On the interaction of solitons for a class of integrable systems in the spacetime R n+1 Letters in Mathematical Physics. ,vol. 26, pp. 199- 209 ,(1992) , 10.1007/BF00420753
Roger G. Newton, Erratum: Inverse Scattering. III. Three dimensions, continued [J. Math. Phys. 22, 2191 (1981)] Journal of Mathematical Physics. ,vol. 23, pp. 693- 693 ,(1982) , 10.1063/1.525386
Sen-yue Lou, Ji Lin, Jun Yu, (3 + 1)-dimensional models with an infinitely dimensional Virasoro type symmetry algebra Physics Letters A. ,vol. 201, pp. 47- 52 ,(1995) , 10.1016/0375-9601(95)00201-D
Senyue Lou, Search for high dimensional integrable models Science China-mathematics. ,vol. 40, pp. 1317- 1324 ,(1997) , 10.1007/BF02876378
Sen-Yue Lou, Jun Yu, Ji Lin, (2+1)-DIMENSIONAL MODELS WITH VIRASORO-TYPE SYMMETRY ALGEBRA Journal of Physics A. ,vol. 28, ,(1995) , 10.1088/0305-4470/28/6/002
Sen-yue Lou, Jian-jun Xu, Higher dimensional Painlevé integrable models from the Kadomtsev–Petviashvili equation Journal of Mathematical Physics. ,vol. 39, pp. 5364- 5376 ,(1998) , 10.1063/1.532576
Richard Beals, Ronald R. Coifman, The D -bar approach to inverse scattering and nonlinear evolutions Physica D: Nonlinear Phenomena. ,vol. 18, pp. 242- 249 ,(1986) , 10.1016/0167-2789(86)90184-3
Roger G. Newton, New result on the inverse scattering problem in three dimensions Physical Review Letters. ,vol. 43, pp. 541- 542 ,(1979) , 10.1103/PHYSREVLETT.43.541