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The Discrete Nonlinear Schrödinger Equation pp 259–275Cite as

Surface Waves and Boundary Effects in DNLS Equations

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Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 232))

Surface waves represent excitations which may propagate along interfaces between different media. These waves occur in diverse areas of physics, chemistry, and iology, often displaying properties that find no counterparts in bulk media [1]. The study of waves on the free surface of water and internal surfaces in stratified liquids is a classical chapter of hydrodynamics. The investigation of surface modes in solidstate physics was initiated by Tamm in 1932, who used the Kronig–Penney model to predict specific electron modes (Tamm states) localized at the edge of the solid [2]. This line of research was extended by Shockley in 1939 [3]. In linear optics, Kossel had predicted the existence of localized states near the boundary between homogeneous and layered media in 1966 [4], which were later observed in AlGaAs multilayer structures [5, 6].

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Author information

Authors and Affiliations

  1. School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, China

    Ying-Ji He

  2. State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou 510275, China

    Ying-Ji He

  3. Department of Physical Electronics, Faculty of Engineering, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel

    Boris A. Malomed

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He, YJ., Malomed, B.A. (2009). Surface Waves and Boundary Effects in DNLS Equations. In: The Discrete Nonlinear Schrödinger Equation. Springer Tracts in Modern Physics, vol 232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89199-4_14

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  • DOI: https://doi.org/10.1007/978-3-540-89199-4_14

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