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The NLS(n, n) equation: Multi-hump compactons and their stability and interaction scenarios

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  • Yan, Zhenya

Abstract

The nonlinear Schrödinger (NLS) equation with fully nonlinear dispersion (called NLS(m, n) equation) has been introduced by Yan [Phys. Lett. A 355 (2006) 212] and shown to possess the single-hump compactons for m=n>1. In this paper, we further investigated the focusing NLS(n, n) equation and find that it possesses the multi-hump compactons for n > 1, whose properties are analyzed in detail. Particularly, we surprisedly find that the maximal intensities of the multi-hump compactons approach to the natural base e as n→1+. Moreover, we numerically study the stabilities and interactions of the single-hump and double-hump compactons such that some stable multi-hump compactons and elastic interactions are found for some small values of the parameter n. These multi-hump compactons will be useful for understanding the soliton-like solutions and applying them in the related fields of nonlinear science.

Suggested Citation

  • Yan, Zhenya, 2019. "The NLS(n, n) equation: Multi-hump compactons and their stability and interaction scenarios," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 25-31.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:25-31
    DOI: 10.1016/j.chaos.2019.03.008
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    Cited by:

    1. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.

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