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Homoclinic solutions of discrete nonlinear Schrödinger equations with asymptotically or super linear terms

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  • Chen, Guanwei
  • Ma, Shiwang

Abstract

In this paper, we study the following periodic discrete nonlinear Schrödinger equation-Δun+(∊n-ω)un=γχngn(un),n∈Z,where the nonlinearity gn is asymptotically or super linear. The sufficient conditions on the existence and on the nonexistence of nontrivial solitons was established by using critical point theory.

Suggested Citation

  • Chen, Guanwei & Ma, Shiwang, 2014. "Homoclinic solutions of discrete nonlinear Schrödinger equations with asymptotically or super linear terms," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 787-798.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:787-798
    DOI: 10.1016/j.amc.2014.01.154
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    References listed on IDEAS

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    1. Jason W. Fleischer & Mordechai Segev & Nikolaos K. Efremidis & Demetrios N. Christodoulides, 2003. "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature, Nature, vol. 422(6928), pages 147-150, March.
    2. Demetrios N. Christodoulides & Falk Lederer & Yaron Silberberg, 2003. "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature, Nature, vol. 424(6950), pages 817-823, August.
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