Solitary solutions to generalized Schrödinger disturbed coupled systems

SHI Juan-rong; ZHU Ming; MO Jia-qi

doi:10.3879/j.issn.1000-0887.2016.03.010

Volume 37 Issue 3

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SHI Juan-rong, ZHU Ming, MO Jia-qi. Solitary solutions to generalized Schrödinger disturbed coupled systems[J]. Applied Mathematics and Mechanics, 2016, 37(3): 319-330. doi: 10.3879/j.issn.1000-0887.2016.03.010

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Solitary solutions to generalized Schrödinger disturbed coupled systems

doi: 10.3879/j.issn.1000-0887.2016.03.010

¹Anhui Technical College of Mechanical and Electrical Engineering, Wuhu, Anhui 241002, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China;³Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China

Funds: The National Natural Science Foundation of China(41275062；11202106)

Received Date: 2015-10-08
Rev Recd Date: 2015-12-02
Publish Date: 2016-03-15

Abstract

Abstract

A class of generalized nonlinear Schrödinger disturbed coupled systems were studied. Firstly, with a special projection method of undetermined coefficients the solitary exact travelling wave solutions to the corresponding nondisturbed coupled systems were found, which were selected as the initial approximation of the disturbed coupled systems. Next, by means of the homotopy analysis method, a set of homotopy mappings were constructed. Thus, each order of the approximate solutions to the original nonlinear Schrödinger disturbed coupled system was obtained successively with the homotopy analysis method. Finally, through the examples and the perturbation theory, it is shown that the acquired approximate solutions to the generalized nonlinear Schrödinger disturbed coupled systems are simple and valid.
- homotopy analysis method,
- soliton,
- coupled system

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References

[1]	McPhaden M J, Zhang D. Slowdown of the meridional overturning circulation in the upper Pacific Ocean[J].Nature,2002,415(3): 603-608.
[2]	Parkes E J. Some periodic and solitary travelling-wave solutions of the short-pulse equation[J].Chaos Solitons Fractals,2008,38(1): 154-159.
[3]	Sirendaorejia, SUN Jiong. Auxiliary equation method for solving nonlinear partial differential equations[J].Physics Letters A,2003,309(5/6): 387-396.
[4]	潘留仙, 左伟明, 颜家壬. Landau-Ginzburg-Higgs方程的微扰理论[J]. 物理学报, 2005,54(1): 1-5.(PAN Liu-xian, ZUO Wei-ming, YAN Jia-ren. The theory of the perturbation for Landau-Ginzburg-Higgs equation[J].Acta Physica Sinica,2005,54(1): 1-5.(in Chinese))
[5]	封国林, 戴新刚, 王爱慧, 丑纪范. 混沌系统中可预报性的研究[J]. 物理学报, 2001,50(4): 606-611.(FENG Guo-lin, DAI Xin-gang, WANG Ai-hui, CHOU Ji-fan. On numerical predictability in the chaos system[J].Acta Physica Sinica,2001,50(4): 606-611.(in Chinese))
[6]	Barbu L, Morosanu G.Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG, 2007.
[7]	de Jager E M, JIANG Fu-ru.The Theory of Singular Perturbation [M]. Amsterdam: North- Holland Publishing, 1996.
[8]	NI Wei-ming, WEI Jun-cheng. On positive solution concentrating on spheres for the Gierer-Meinhardt system[J].Journal of Differential Equations,2006,221(1): 158-189.
[9]	Bartier J P. Global behavior of solutions of a reaction-diffusion equation with gradient absorption in unbounded domains[J].Asymptotic Analysis,2006,46(3/4): 325-347.
[10]	Libre J, da Silva P R, Teixeira M A. Regularization of discontinuous vector fields on R³ via singular perturbation[J].Journal of Dynamics & Differential Equations,2007,19(2): 309-331.
[11]	Guarguaglini F R, Natalini R. Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena[J].Communications in Partial Differential Equations,2007,32(2): 163-189.
[12]	LIAO Shi-jun. Proposed homotopy analysis techniques for the solution of nonlinear problems[D]. PhD Thesis. Shanghai: Shanghai Jiao Tong University, 1992.
[13]	Shao S. Asymptotic analysis and domain decomposition for a singularly perturbed reaction-convection-diffusion system with shock-interior layer interactions[J].Nonlinear Analysis: Theory, Methods &Applications,2007,66(2): 271-287.
[14]	LIAO Shi-jun. On the homotopy analysis method for nonlinear problems[J].Applied Mathematics and Computation,2004,147(12): 499-513.
[15]	Liao S J.Beyond Perturbation: Introduction to the Homotopy Analysis Method [M]. New York: CRC Press Co, 2004.
[16]	廖世俊. 超越摄动: 同伦分析方法基本思想及其应用[J]. 力学进展, 2008,38(1): 1-34.(LIAO Shi-jun. Beyond perturbation: the basic concepts of homotopy analysis method and its applications[J]. Advances in Mechanics,2008,38(1): 1-34.(in Chinese))
[17]	LIAO Shi-jun. An optimal homotopy-analysis approach for strongly nonlinear differential equations[J].Communications in Nonlinear Science and Numerical Simulation,2010,15(8): 2003-2016.
[18]	LIAO Shi-jun.Homotopy Analysis Method in Nonlinear Differential Equations[M]. Heidelberg: Springer & Higher Education Press, 2012.
[19]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China(Ser A),1989,32(11): 1306-1315.
[20]	MO Jia-qi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J].Science in China(Ser G): Physics, Mechanics & Astronomy,2009,39(7): 1007-1010.
[21]	莫嘉琪, 陈贤峰. 一类广义非线性扰动色散方程孤立波的近似解[J]. 物理学报, 2010,50(3): 1403-1408.(MO Jia-qi, CHEN Xian-feng. Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation[J].Acta Physica Sinica,2010,50(3): 1403-1408.(in Chinese))
[22]	MO Jia-qi, LIN Su-rong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J].Chinese Physics B,2009,18(9): 3628-3631.
[23]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J].Communications in Theoretical Physics,2011,55(3): 387-390.
[24]	MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J].Chinese Physics B,2010,19(10): 100203-1-100203-4.
[25]	史娟荣, 石兰芳, 莫嘉琪. 一类非线性强阻尼扰动发展方程的解[J]. 应用数学和力学, 2014,35(9): 1046-1054.(SHI Juan-rong, SHI Lan-fang, MO Jia-qi. Solutions to a class of nonlinear strong-damp disturbed evolution equations[J].Applied Mathematics and Mechanics,2014,35(9): 1046-1054.(in Chinese))
[26]	史娟荣, 吴钦宽, 莫嘉琪. 非线性扰动广义NNV系统的孤立子渐近行波解[J]. 应用数学和力学, 2015,36(9): 1003-1010.(SHI Juan-rong, WU Qin-kuan, MO Jia-qi. Asymptotic travelling wave soliton solutions for nonlinear disturbed generalized NNV systems[J].Applied Mathematics and Mechanics,2015,36(9): 1003-1010.(in Chinese))
[27]	SHI Juan-rong, LIN Wan-tao, MO Jia-qi. The singularly perturbed solution for a class of quasilinear nonlocal problem for higher order with two parameters[J].Acta Scientiarum Naturalium Universitatis Nakaiensis,2015,48(1): 85-91.
[28]	马松华, 方建平. 联立薛定谔系统新精确解及其所描述的孤子脉冲和时间孤子[J]. 物理学报, 2006,55(11): 5611.(MA Song-hua, FANG Jian-ping. New exact solutions for the related Schr?dinger equation and the temporal-soliton and soliton-impulse[J].Acta Physica Sinica,2006,55(11): 5611.(in Chinese))
[29]	李帮庆, 马玉兰, 徐美萍, 李阳. 耦合Schrdinger系统的周期振荡折叠孤子[J]. 物理学报, 2011,60(6): 060203.(LI Bang-qing, MA Yu-lan, XU Mei-ping, LI Yang. Folded soliton with periodic vibration for a nonlinear coupled Schr?dinger system[J].Acta Physica Sinica,2011,60(6): 060203.(in Chinese))