Skip to main content
SpringerLink
Log in

Discrete nonlinear excitations on an inhomogeneous lattice in a spatially linear potential

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

Discrete nonlinear excitations on an inhomogeneous lattice in a spatially linear potential are investigated. Discrete breathers possessing multiple frequencies are always spatially localized and oscillatory in time, with oscillatory frequencies depending on an external potential. A number of phenomena associated with the translational symmetry of the system is addressed. The spatially localized, time periodic and quasi-periodic nonlinear coherent excitations comprising multiple-soliton components are presented with exact results for the corresponding energy, momentum and norm. The mean width of a pulse as a measure of localization is also studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bishop, A.R., Ecke, K., Gubernatis, J., eds., Nonlinearity in materials science,Physica, 1993, (1–2): 66.

  2. Christiansen, P. L., Eilberk, J. C., Parmentier, R. V., eds., Future directions of nonlinear dynamics in physics and bio- logical systems,Physica,D, 1993, (1–2): 68.

  3. Scharf, R., Bishop, A. R., Properties of the nonlinear Schrodinger equation on a lattice,Phys. Rev. A, 1991, 43: 6535.

    Article  MathSciNet  Google Scholar 

  4. Ablowitz, M. J., Ladik, J. F., Nonlinear differential-difference equations,J. Math.Phys., 1975, 16: 698.

    MathSciNet  Google Scholar 

  5. Ablowitz, M. J., Ladik, J. F., Nonlinear differential-differences equations and Fourier analysis,J.Math. Phys., 1976, 17: 1011.

    Article  MATH  MathSciNet  Google Scholar 

  6. Cai, D., Bishop, A. R., Gronbech-Jensen, N. et al., Electric-field-induced nonlinear block oscillations and dynamical local- ization,Phys. Rev. Lett., 1994, 72: 591.

    Article  Google Scholar 

  7. Cai, D., Bishop, A. R., Gronbech-Jensen, N. et al., Localized states in discrete nonlinear Shrodinger equations,Phys. Rev. Lett., 1998, 74: 1186.

    Article  Google Scholar 

  8. Cai, D., Bishop, A. R., Gronbech-Jensen, N., Spatically localized, temporally quisiperiodic, discrete nonlinear excitations,Phys. Rev., 1998, 52: R5784.

    Google Scholar 

  9. Cai, D., Bishop, A. R., Gronbech-Jensen, N., Discrete lattice effects on breathers in a spatially linear potential,Phys. Rev., 1996, 53: 1202.

    MathSciNet  Google Scholar 

  10. Cai, D., Bishop, A. R., Gronbech-Jensen, N., Perturbation theories of a discrete, integrable nonlinear Schrodinger equa- tion,Phys. Rev., 1996, 53: 4131.

    MathSciNet  Google Scholar 

  11. Konotop, V. V., Soliton on a disordered lattice,Phys. Rev., Ser. E, 1993, 47: 1423.

    Article  Google Scholar 

  12. Konotop, V. V., Chubykalo, O. A., Vazquez, L., Dynamics and interaction of solitons on an integrable inhomogeneous lat- tice,Phys. Rev., Ser. E, 1993, 48: 563.

    Article  Google Scholar 

  13. Herbst, B. M., Ablowitz, M. J., Numerically induced chaos in the nonlinear Schrodinger equation,Phys. Rev. Lett., 1989, 62: 2065

    Article  MathSciNet  Google Scholar 

  14. Dunlap, D. H., Kenkre, V. M., Effect of scattering on the dynamic localization of a particle in a time-dependent electric field,Phys. Rev. B, 1986, 34: 3625.

    Article  Google Scholar 

  15. Hirota, R.,Solitons (eds. Bullough, R. K., Caudrey, P. J.), New York: Springer-Verlag, 1980.

    Google Scholar 

  16. Tikhonov, A. N., Vasileva, A. B., Sveshnikov, A. G.,Differential Equations, Munich: Springer-Verlag, 1980.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Chinese Academy of Sciences, 100080, Beijing, China

    Wuming Liu

  2. Institute of Acoustics, Chinese Academy of Sciences, 100080, Beijing, China

    Ke Liu

  3. Institute of Applied Physics and Computational Mathematics, 100088, Beijing, China

    Xiangeng Zhao

  4. Institute of Theoretical Physics, Chinese Academy of Sciences, 100080, Beijing, China

    Xiangeng Zhao

Authors
  1. Wuming Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangeng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, W., Liu, K. & Zhao, X. Discrete nonlinear excitations on an inhomogeneous lattice in a spatially linear potential. Sci. China Ser. A-Math. 41, 285–295 (1998). https://doi.org/10.1007/BF02879047

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02879047

Keywords

Search

Navigation