The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice

Chinese Science Bulletin

Volumn 50, Issue 1, 2005, Pages 5-10

  Xu, Quan ^a   Tian, Qiang ^b  

^a Daqing Teachers College   (China)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Multiple scale method; The solutions perturbed by the neck mode; Two dimensional discrete soliton trains; Two dimensional nonlinear lattice

Indexed keywords

EID: 33749673598     PISSN: 10016538     EISSN: 18619541     Source Type: Journal    
DOI: 10.1360/04ww0068     Document Type: Article

References (27)

1. Tian, Q., Zhou, H., Zhu, R., A theoretical description for solitons in polyacetylene, Science in China, Ser. A, 2002, 54(7): 884-887.
2. Tian, Q., Wu, C. S., Solitons in superlattices: A tight-binding approach, Phys. Lett., 1999, A262: 83.
3. Kivshar, Y. S., Self-induced gap solitons, Phys. Rev. Lett., 1993, 70: 3055.
4. Alfimov, G., Konotop, V. V., On the existence of gap, Physica, 2000, D146: 307.
5. Bang, O., Christiansen, P. L., IF. F. et al., White noise in the two-dimensional nonlinear Schrodinger equation, Applicable Analysis, 1995, 57: 3-15.
6. Ablowitz, M. J., Clarkson, P. A., Solitons, nonlinear evolution equations and inverse scattering, London Mathematical Society Note Series, 1991, 149: 17-179.
7. Anders, I., Asymptotics of the coupled solutions of the modified Kadomtsev-Petnashvili equation, Proceedings of Institute of Mathematics of NAS of Ukraine, 2002, 43(1): 291-295.
8. Zakharov, V., Shock waves propagated on solitons on the surface of a fluid, Izv. Vyszh. Vchebn. Zaved. Radiofiz, 1986, 29(9): 1073.
9. Anders, I., Kotlyaroy, V., Khruslov, E., Cumed asymptotic solitons of the Kadomtsev Petviashvili equation, Theor. Math. Phys., 1994, 99: 402.
10. Masayoshi Tajiri, Hiroyuki Miura, Takahito Arai, Resonant interaction of modulational instability with a periodic soliton in the Devey-Stevartson equation, Phys. Rev., 2002, E66: 067601.
11. Remoissenet, M., Waves Called Solitons, Berlin-Heidelberg-New York: Springer-Verlag, 1996, 138-204.
12. Sulem, P. L., Sulem, C., Nonlinear Schrodinger Equation: Self-focusing and Wave Collapse, New York: Springer-Verlag, 1999.
13. Yoshida, H., Construction of higher order symplectic integrators, Phys. Lett., 1990, A150: 262-268.
14. Carter, J. D., Segur, H., Instabilities in the two-dimensional cubic nonlinear Schrodinger equation, Phys. Rev., 2003, E68: 045601.
15. Manakov, S. V., On the theory of two-dimensional stationary self-focusing of electromagnetic manes, Sov. Phys. JETP, 1974, 38: 232-240.
16. Benney, D. J., Roshes, G. J., Wave instabilities, Studies in Applied Mathematics, 1969, 48: 377.
17. Davey, A., Stemartson, K., On three-dimensional packets of surface waves, Proc. R. Soc. London Ser., 1974, A338: 101-110.
18. Pecseli, H. L., Solitons and weakly nonlinear waves in plasmas, IEEE Transactions on Plasma Science, 1985, 13: 53-86.
19. Donnelly, R., Quantized Vortices in Helium IR, Cambridge: Cambridge University Press, 1991.
20. Gross, E. P., Hydrodynamics of a superfluid condensate, Math. Phys., 1963, 4: 195.
21. Pitaevskii, L. P., Vortex linex in an imperfect Bose gas, Sov. Phys. JETP, 1961, 13: 451.
22. Zahkarov, V. E., Shabat, A. B., Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of manes in nonlinear media, Sov. Phys. JETP, 1972, 34: 62-69.
23. Zahkarov, V. E., Shabat, A. B., On interactions between solitons in a stable medium, Sov. Phys. JETP, 1973, 37: 823-828.
24. Yang Jianke, Ziad, H. M., Fundamental and vortex solitons in a two-dimensional optical lattice, Opt. Lett. 2003, 28(21): 2094-2096.
25. Chen Zhigang, Hector, M., Eugenia, D. E. et al., Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains, Phys. Rew. Lett., 2004, 92(14): 143902.
26. Zahkarov, V. E., Rubenchik, A. M., Instability of waveguides and solitons in nonlinear media, Sov. Phys. JETP, 1974, 38: 494-500.
27. Hennig, D., Tsironis, G. P., Wave transmission in nonlinear lattice, Phys. Rep., 1999, 307: 333-432.