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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 10
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Original Articles

Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization

Pages 1591-1602 | Received 08 Feb 2010, Accepted 30 Apr 2010, Published online: 15 Sep 2010

References

  • Kevrekidis , P , Rasmussen , K and Bishop , A . 2001 . The discrete nonlinear Schrödinger equation: A survey of recent results . Int. J. Mod. Phys. B , 15 : 2833 – 2900 .
  • Eilbeck , J and Johansson , M . The discrete nonlinear Schrödinger equation – 20 years on, in Proceedings of the Third Conference on Localization and Energy Transfer in Nonlinear Systems 2002, 2003, pp. 44–87
  • Kevrekidis , P . 2009 . Springer tracts in modern physics, 1. General introduction and derivation of the DNLS equation in The Discrete Nonlinear Schrödinger Equation Vol. 232 , 3 – 9 . Berlin : Springer .
  • Porter , M . 2009 . “ Experimental results related to DNLS equation ” . In The Discrete Nonlinear Schrödinger Equation , Edited by: Kevrekidis , P . 175 – 189 . Berlin : Springer .
  • Pacciani , P , Konotop , V and Menzala , GP . 2005 . On localized solutions of discrete nonlinear Schrödinger equation. An exact result . Physica D , 204 : 122 – 133 .
  • Guérékata , G and Pankov , A . 2010 . Global well-posedness for discrete nonlinear Schrödinger equation . Appl. Anal. , 89 ( 9 ) : 1513 – 1521 .
  • Kevrekidis , P . 2009 . Springer tracts in modern physics, 2. The one-dimensional case, in The Discrete Nonlinear Schrödinger Equation , Edited by: Kevrekidis , P . Vol. 232 , 3 – 9 . Berlin : Springer .
  • Kevrekidis , P . 2009 . Springer tracts in modern physics, 5. The defocusing case, in The Discrete Nonlinear Schrödinger Equation , Edited by: Kevrekidis , P . Vol. 232 , 117 – 141 . Berlin : Springer .
  • Herrmann , M . Homoclinic standing waves in focussing DNLS equations, (2010), preprint, see arXiv:1002.1590
  • MacKay , R and Aubry , S . 1994 . Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators . Nonlinearity , 7 : 1623 – 1643 .
  • Aubry , S . 1997 . Breathers in nonlinear lattices: Existence, linear stability and quantization . Physica D , 103 : 201 – 250 .
  • Kevrekidis , P and Law , K . 2009 . “ Numerical methods for DNLS ” . In The Discrete Nonlinear Schrödinger Equation , Edited by: Kevrekidis , P . 191 – 203 . Berlin : Springer .
  • Pelinovsky , D and Rothos , V . 2005 . Bifurcations of travelling wave solutions in the discrete NLS equations . Physica D , 202 : 16 – 36 .
  • Pankov , A and Zakharchenko , N . 2001 . On some discrete variational problems . Acta Appl. Math. , 65 : 295 – 303 .
  • Pankov , A and Rothos , V . 2008 . Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity . Proc. R. Soc. A , 464 : 3219 – 3236 .
  • Zhang , G and Pankov , A . 2010 . Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials . Appl. Anal. , 89 ( 9 ) : 1541 – 1557 .
  • Zhang , G and Liu , F . 2009 . Existence of breather solutions of the DNLS equations with unbounded potentials . Nonlinear Anal. Theory Methods Appl. , 71 : e786 – e792 .
  • Pankov , A . 2006 . Gap solitons in periodic discrete nonlinear Schrödinger equations . Nonlinearity , 19 : 27 – 40 .
  • Pankov , A . 2007 . Gap solitons in periodic discrete nonlinear Schrödinger equations II: A generalized Nehari manifold approach . Discret. Contin. Dyn. Syst. , 19 : 419 – 430 .
  • Pankov , A . Gap solitons in periodic discrete nonlinear Schrödinger equations with saturable nonlinearity, (2010), preprint
  • Fečkan , M and Rothos , V . 2010 . Travelling waves of discrete nonlinear Schrödinger equations with nonlocal interactions . Appl. Anal. , 89 ( 9 ) : 1387 – 1411 .

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