Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 071, 16 pages      arXiv:1704.07003      https://doi.org/10.3842/SIGMA.2017.071
Contribution to the Special Issue on Symmetries and Integrability of Difference Equations

$N$-Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schrödinger Equation

Bao-Feng Feng a and Yasuhiro Ohta b
a) School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
b) Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan

Received April 25, 2017, in final form September 03, 2017; Published online September 06, 2017

Abstract
In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota's bilinear method. One- and two-bright-dark soliton solutions are explicitly presented for two-component semi-discrete NLS equation; two-bright-one-dark, and one-bright-two-dark soliton solutions are also given explicitly for three-component semi-discrete NLS equation. The asymptotic behavior is analysed for two-soliton solutions.

Key words: bright-dark soliton; semi-discrete vector NLS equation; Hirota's bilinear method; Pfaffian.

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