Skip to main content

Solitary wave solutions to the discrete nonlinear Schrödinger equation

  • Part III: Lattice Excitations and Localised Modes
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 393))

Abstract

The existence of various solitary wave solutions to the (nonintegrable) discrete nonlinear Schrödinger equation is demonstrated numerically.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A S Davydov and N I Kislukha. Solitary excitons in one-dimensional molecular chains. Phys. Stat. Sol. (b), 59:465–470, 1973.

    Google Scholar 

  2. P Baňacký and A Zajac. Theory of particle transfer dynamics in solvated molecular complexes: analytic solutions of the discrete time-dependent nonlinear Schrödinger equation. I. conservative system. Chem. Phys., 123:267–276, 1988.

    Article  Google Scholar 

  3. D N Christodoulides and R I Joseph. Discrete self-focussing in nonlinear arrays of coupled waveguides. Optics Letters, 13:794–796, 1988.

    Google Scholar 

  4. H-L Wu and V M Kenkre. Generalized master equations from the nonlinear Schrödinger equation and propagation in an infinite chain. Phys. Rev. B, 39:2664–2669,1989.

    Article  Google Scholar 

  5. A C Scott, F Y F Chu, and D W McLaughlin. The soliton: a new concept in applied science. Proc. IEEE, 61:1443–1483, 1973.

    Google Scholar 

  6. J C Eilbeck. Numerical simulations of the dynamics of polypeptide chains and proteins. In Chikao Kawabata and A R Bishop, editors, Computer Analysis for Life Science — Progress and Challenges in Biological and Synthetic Polymer Research, pages 12–21, Tokyo, 1986. Ohmsha.

    Google Scholar 

  7. J C Eilbeck. Numerical studies of solitons on lattices. (These proceedings), 1991.

    Google Scholar 

  8. H B Keller. Numerical solution of bifurcation and nonlinear eigenvalue problems. In P H Rabinowitz, editor, Applications of Bifurcation Theory, New York, 1977. Academic.

    Google Scholar 

  9. D W Decker and H B Keller. Path following near bifucation. Comm. Pure Appl. Math., 34:149–175, 1981.

    Google Scholar 

  10. J C Eilbeck. The pseudo-spectral method and path following in reaction-diffusion bifurcation studies. SIAM J. Sci. Statist. Comput., 7:599–610, 1986.

    Google Scholar 

  11. J C Eilbeck and R Flesch. Calculation of families of solitary waves on discrete lattices. Phys. Lett. A, 149:200–202, 1990.

    Google Scholar 

  12. J C Eilbeck, P S Lomdahl, and A C Scott. The discrete self-trapping equation. Physica D: Nonlinear Phenomena, 16:318–338, 1985.

    Google Scholar 

  13. V M Kenkre. The discrete nonlinear Schrödinger equation: nonadiabatic effects, finite temperature consequences, and experimental manifestations. In P L Christiansen and A C Scott, editors, Davydov's soliton revisited, London, 1990. Plenum. (To be published).

    Google Scholar 

  14. L Cruzeiro-Hansson, H Feddersen, R Flesch, P L Christiansen, M Salerno, and A C Scott. Classical and quantum analysis of chaos in the discrete self-trapping equation. Phys. Rev. B, 42:522–526, 1990.

    Google Scholar 

  15. M J Ablowitz and J F Ladik. A nonlinear difference scheme and inverse scattering. Stud. Appl. Math., 55:213–229, 1976.

    Google Scholar 

  16. M J Ablowitz and J F Ladik. Nonlinear differential-difference equations and Fourier analysis. J. Math. Phys., 17:1011–1018, 1976.

    Article  Google Scholar 

  17. P G Drazin. Solitons. Cambridge Univ. Press, Cambridge, 1983.

    Google Scholar 

  18. A V Zolotariuk and A V Savin. Solitons in molecular chains with intramolecular nonlinear interactions. Physica D, 46:295–314, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. Remoissenet M. Peyrand

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Feddersen, H. (1991). Solitary wave solutions to the discrete nonlinear Schrödinger equation. In: Remoissenet, M., Peyrand, M. (eds) Nonlinear Coherent Structures in Physics and Biology. Lecture Notes in Physics, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54890-4_167

Download citation

  • DOI: https://doi.org/10.1007/3-540-54890-4_167

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54890-4

  • Online ISBN: 978-3-540-46458-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics