Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

doi:10.1007/s10483-012-1645-7

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (12): 1583-1594.doi: https://doi.org/10.1007/s10483-012-1645-7

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

姚静荪¹, 欧阳成², 陈丽华³, 莫嘉琪^1,2

1. Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui Province, P. R. China;
2. Faculty of Science, Huzhou Teacher College, Huzhou 313000, Zhejiang Province, P. R. China;
3. Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing 350300, Fujian Province, P. R. China

收稿日期:2011-10-12 修回日期:2012-05-24 出版日期:2012-12-10 发布日期:2012-12-10
通讯作者: Jing-sun YAO, Professor, E-mail: jsyao@mail.ahnu.edu.cn E-mail:jsyao@mail.ahnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 41175058), the “Strategic Priority Research Program-Climate Change: Carbon Budget and Relevant Issues” of the Chinese Academy of Sciences (No.XDA01020304), the Natural Science Foundation from the Education Bureau of Anhui Province of China (No.KJ2011A135), the Natural Science Foundation of Zhejiang Province of China (No.Y6110502), the Foundation of the Education Department of Fujian Province of China (No. JA10288), and the Natural Science Foundation of Jiangsu Province of China (No.BK2011042)

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

Jing-sun YAO¹, Cheng OU-YANG², Li-hua CHEN³, Jia-qi MO^1,2

1. Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui Province, P. R. China;
2. Faculty of Science, Huzhou Teacher College, Huzhou 313000, Zhejiang Province, P. R. China;
3. Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing 350300, Fujian Province, P. R. China

Received:2011-10-12 Revised:2012-05-24 Online:2012-12-10 Published:2012-12-10
Supported by:
Project supported by the National Natural Science Foundation of China (No. 41175058), the “Strategic Priority Research Program-Climate Change: Carbon Budget and Relevant Issues” of the Chinese Academy of Sciences (No.XDA01020304), the Natural Science Foundation from the Education Bureau of Anhui Province of China (No.KJ2011A135), the Natural Science Foundation of Zhejiang Province of China (No.Y6110502), the Foundation of the Education Department of Fujian Province of China (No. JA10288), and the Natural Science Foundation of Jiangsu Province of China (No.BK2011042)

摘要/Abstract

摘要： A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.

关键词: generalized cell mapping, multiple-attractor coexisting system, parameter uncertainties

Abstract: A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.

Key words: generalized cell mapping, multiple-attractor coexisting system, parameter uncertainties

中图分类号:

O175

姚静荪;欧阳成;陈丽华;莫嘉琪. Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1583-1594.

Jing-sun YAO;Cheng OU-YANG;Li-hua CHEN;Jia-qi MO. Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1583-1594.

参考文献

[1] Parkes, E. J., Duffy, B. R., and Abbott, P. C. Some periodic and solitary travelling-wave solutionsof the short-pulse equation. Chaos, Solitons and Fractals, 38(1), 154-159 (2008)
[2] Sirendaoreji, J. S. Auxiliary equation method for solving nonlinear partial differential equations.Phys. Lett. A, 309(5-6), 387-396 (2003)
[3] McPhaden, M. J. and Zhang, D. Slowdown of the meridional overturning circulation in the upperPacific Ocean. nature, 415(3), 603-608 (2002)
[4] Pan, L. S., Zou, W. M., and Yan, J. R. The theory of the perturbation for Landau-Ginzburg-Higgsequation (in Chinese). Acta Phys. Sin., 54(1), 1-5 (2005)
[5] Feng, G. L., Dai, X. G., Wang, A. H., and Chou, J. F. On numerical predictability in the chaossystem (in Chinese). Acta Phys. Sin., 50(4), 606-611 (2001)
[6] Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press Co.,New York (2004)
[7] He, J. H. and Wu, X. H. Construction of solitary solution and compacton-like solution by variationaliteration method. Chaos, Solitions and Fractals, 29(1), 108-113 (2006)
[8] Ni, W. M. and Wei, J. C. On positive solution concentrating on spheres for the Gierer-Meinhardtsystem. Journal of Differential Equations, 221(1), 158-189 (2006)
[9] Bartier, J. P. Global behavior of solutions of a reaction-diffusion equation with gradient absorptionin unbounded domains. Asymptotic Analysis, 46(3-4), 325-347 (2006)
[10] Libre, J., da Silva, P. R., and Teixeira, M. A. Regularization of discontinuous vector fields on R3via singular perturbation. Journal of Dynamics and Differential Equations, 19(2), 309-331 (2007)
[11] Guarguaglini, F. R. and Natalini, R. Fast reaction limit and large time behavior of solutions toa nonlinear model of sulphation phenomena. Communication in Partial Differential Equations,32(2), 163-189 (2007)
[12] Mo, J. Q. Singular perturbation for a class of nonlinear reaction diffusion systems. Science inChina, Ser. A, 32(11), 1306-1315 (1989)
[13] Mo, J. Q. Homotopic mapping solving method for gain fluency of laser pulse amplifier. Science inChina, Ser. G, 39(5), 568-661 (2009)
[14] Mo, J. Q., Lin, Y. H., and Lin, W. T. Approximate solution of sea-air oscillator for El Ei Ni?no-southern oscillation model (in Chinese). Acta Phys. Sin., 59(10), 6707-6711 (2010)
[15] Mo, J. Q. and Lin, S. R. The homotopic mapping solution for the solitary wave for a generalizednonlinear evolution equation. Chin. Phys. B, 18(9), 3628-3631 (2009)
[16] Mo, J. Q. Solution of travelling wave for nonlinear disturbed long-wave system. Commun. Theor.Phys., 55(3), 387-390 (2011)
[17] Mo, J. Q. and Chen, X. F. Homotopic mapping method of solitary wave solutions for generalizedcomplex Burgers equation. Chin. Phys. B, 19(10), 100203 (2010)
[18] Li, B. Q., Ma, Y., Wang, C., Xu, M. P., and Li, Y. G′/G-expansion method and novel fractalstructures for high-dimensional nonlinear physical equation (in Chinese). Acta Phys. Sin., 60(63),060203 (2011)
[19] Barbu, L. and Morosanu, G. Singularly Perturbed Boundary-Value Problems, Birkhäuser Basel,Basel (2007)
[20] De Jager, E. M. and Jiang, F. R. The Theory of Singular Perturbation, North-Holland Publishing,Amsterdam (1996)

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

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