二维分立单原子晶格非线性振动的特性被引量：1

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摘要运用多重尺度方法及准分立近似,求解二维单原子晶格的非线性振动方程,在只考虑最近邻相互作用下,二维单原子晶格的非线性振动特性由二维CNLS(CubicNonlinearSchrodinger)方程描述.具有二维分立孤子拖曳解和颈模型摄动解.

作者徐权田强

机构地区大庆师范学院科研处北京师范大学物理系

出处《科学通报》 EI CAS CSCD 北大核心 2005年第1期6-11,共6页 Chinese Science Bulletin

关键词单原子非线性振动二维近似晶格孤子摄动解方程品格描述

参考文献27

1田强,周会,朱瑞.聚乙炔中孤子的理论分析[J].中国科学（A辑）,2002,32(6):574-576. 被引量：2
2Tian Q, Wu C S. Solitons in superlattices: A tight-binding ap-proach. Phys Lett, 1999, A262:83.
3Yuri S Kivshar. Self-induced gap solitons. Phys Rev Lett, 1993,70:3055.
4Alfimov G, Konotop V V. On the existence of gap. Physica, 2000,D146:307.
5Bang O, Christiansen P L, IF F, et al. White noise in the two-dimensional nonlinear schrodinger equation. Applicable Analysis, 1995, 57:3-15.
6Ablowitz M J, Clarkson P A. Solitons nonlinear evolution equa-tions and inverse scattering. London Mathematical Society Note Series, 1991, 149:17-179.
7Anders I. Asymptotics of the coupled solutions of the modified Kadomtsev-Petnashvili equation. Proceedings of Institute ofMathematics of NAS of Ukraine, 2002, 43(1): 291-295.
8Zakharov V. Shock waves propageted on solitons on the surface of a fluid. Izv Vyszh Vchebn Zaved Radiofiz, 1986, 29(9): 1073.
9Anders I, Kotlyaroy V, Khruslov E. Curned asymptotic solitons of the Kadomtsev Petviashvili equation. Theor Math Phys, 1994,99(1): 402.
10Masayoshi Tajiri, Hiroyuki Miura, Takahito Arai. Resonant inter-action of modulational instability with a periodic soliton in the Devey-Stevartson equation. Phys Rev, 2002, E66:067601.

1[1]Ladik J J. Polymers as solids: a quantum mechanical treatment. Physics Report, 1999, 313: 171～235
2[2]Heeger A J, Kivelson S, Schrieffer J R, et al. Solitons in conducting polymers. Rev Mod Phys, 1988, 60: 781～850
3[3]Peierls R E. Quantum Theory of Solids. Oxford: Oxford University Press, 1955. 108～118
4[4]Hayes W. Conducting polymers. Contemp Phys, 1985, 26: 421～441
5[5]Salaneck W R. Conformational defects in a conducting polymer. Contemp Phys, 1989, 30: 403～416
6[6]Su W P, Schrieffer J R, Heeger A J. Solitons in polyacetylene. Phys Rev Lett, 1979, 42: 1698～1701
7[7]Su W P, Schrieffer J R, Heeger A J. Soliton excitations in polyacetylene. Phys Rev B, 1980, 22: 2099～2111
8[8]Tian Q, Ma B K. Solitons in superlattices. Physica A, 1998, 259: 59～64
9[9]Tian Q, Wu C S. Solitons in superlattices: A tight-binding approach. Phys Lett A, 1999, 262: 83～85
10[10]Sterke C M, Sipe J E. Envelope-function approach for the electrodynamics of nonlinear periodic structures. Phys Rev A, 1988, 38: 5149～5165

1徐权.一维非线性单原子分立晶格振动的格孤波解和非传播呼吸子解[J].佳木斯大学学报（自然科学版）,2004,22(3):354-357. 被引量：1
2徐权,田强.一维分子链中激子与声子的相互作用和呼吸子解[J].物理学报,2004,53(9):2811-2815. 被引量：1
3徐权.长波近似下一维双原子链非线性振动的特征[J].高师理科学刊,2004,24(3):28-32. 被引量：1
4徐权,田强.准一维单原子非线性晶格振动的扭结孤子解和反扭结孤子解[J].中国科学（G辑）,2004,34(6):648-654. 被引量：3
5TIAN Q, WU C S. Solitons in superlattices: a tight-binding approach [J]. Phys Lett, 1999, A262: 83-85.
6NESHEV D N, ALEXANDER T J, OSTROVSKAYA E A, et al. Observation of discrete vortex solitons in optically induced photonic lattice [J]. Phys Rev Lett, 2004, 92(12): 123903-1-123903-4.
7FLACH S, WILLIS C R. Discrete breathers [J]. Phys Rep, 1998, 295: 181-264.
8BANG O, CHRISTIANSEN P L, IF F, et al. White noise in the two-dimensional nonlinear schrodinger equation [J]. Appl Anal, 1995, 57: 3-15.
9KIVSHAR Y S. Self-induced gap solitons [J]. Phys Rev Lett, 1993, 70(20) : 3055-3058.
10ALFIMOV G, KONOTOP V V. On the existence of gap [J]. Physica, 2000, D146: 307-327.

1徐权,田强.准一维单原子非线性晶格振动的扭结孤子解和反扭结孤子解[J].中国科学（G辑）,2004,34(6):648-654. 被引量：3
2徐权,夏遵义.二维单原子晶格的非线性振动线孤子解[J].齐齐哈尔大学学报（自然科学版）,2004,20(2):66-68.
3张园,欧阳成.一类非线性系统的可解性条件与渐近解[J].数学的实践与认识,2013,43(22):213-217.
4张蔚曦,王登龙,丁建文.准二维凝聚体中暗孤子环的动力学演化[J].物理学报,2008,57(11):6786-6791. 被引量：1
5卢祥虎,张艳丹,江新华.Schnakenberg方程解的渐近分析[J].数学计算（中英文版）,2014,3(2):68-75. 被引量：2
6杨良梁,徐权,田强.二维单原子晶格非线性振动的扭结孤子解[J].扬州大学学报（自然科学版）,2005,8(1):18-22.
7杨晓东,林志华.利用多尺度方法分析基于非局部效应纳米梁的非线性振动[J].中国科学：技术科学,2010,40(2):152-156. 被引量：9
8翟孝月,李延标,马书云.横场中各向异性XY模型的部分熵和量子互熵[J].南京师大学报（自然科学版）,2012,35(3):48-51.
9张道华,李华新,朱国良,石大庆,李金星.一维FPU晶格模型中的孤子研究[J].湖北师范学院学报（自然科学版）,2013,33(4):5-8.
10王春花,谢定一,占丽萍,张李攀,赵良珮.SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHR?DINGER SYSTEMS IN R^2[J].Acta Mathematica Scientia,2015,35(2):383-398.

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2005年第1期

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