Citation: | 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 |
[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Schrdinger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))
|