About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 842594, 6 pages
http://dx.doi.org/10.1155/2013/842594
Research Article

Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials

1School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 18 January 2013; Accepted 25 February 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Meihua Huang and Zhan Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Belmonte-Beitia, V. M. Pérez-García, and P. J. Torres, “Solitary waves for linearly coupled nonlinear Schrödinger equations with inhomogeneous coefficients,” Journal of Nonlinear Science, vol. 19, no. 4, pp. 437–451, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, “Production of two overlapping Bose-Einstein condensates by sympathetic cooling,” Physical Review Letters, vol. 78, no. 4, pp. 586–589, 1997. View at Scopus
  3. R. S. MacKay and S. Aubry, “Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators,” Nonlinearity, vol. 7, no. 6, pp. 1623–1643, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Aubry, “Breathers in nonlinear lattices: existence, linear stability and quantization,” Physica D, vol. 103, no. 1–4, pp. 201–250, 1997, Lattice dynamics (Paris, 1995). View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. G. Kevrekidis, The Discrete Nonlinear Schrödinger Equation, Springer, 2009.
  6. D. E. Pelinovsky and V. M. Rothos, “Bifurcations of travelling wave solutions in the discrete NLS equations,” Physica D, vol. 202, no. 1-2, pp. 16–36, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Pankov and V. Rothos, “Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity,” Proceedings of The Royal Society of London A, vol. 464, no. 2100, pp. 3219–3236, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Shi and H. Zhang, “Existence of gap solitons in a periodic discrete nonlinear Schrödinger equations,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 254–265, 2010.
  9. G. Zhang and F. Liu, “Existence of breather solutions of the DNLS equations with unbounded potentials,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 12, pp. e786–e792, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. Zhou and J. Yu, “On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems,” Journal of Differential Equations, vol. 249, no. 5, pp. 1199–1212, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. Zhou, J. Yu, and Y. Chen, “On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity,” Nonlinearity, vol. 23, no. 7, pp. 1727–1740, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Liu, W. Yan, and X. Zhao, “The existence of standing wave for the discrete coupled nonlinear Schrödinger lattice,” Physics Letters A, vol. 374, no. 15-16, pp. 1690–1693, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet