TY - JOUR
T1 - Riemann-Hilbert Approach and Soliton Solutions of the Higher-Order Dispersive Nonlinear Schrödinger Equations with Single and Double Poles
AU - Li , Zhi-Qiang
AU - Tian , Shou-Fu
AU - Yang , Jin-Jie
AU - Wang , Xiao-Li
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 369
EP - 388
PY - 2021
DA - 2021/02
SN - 11
DO - http://doi.org/10.4208/eajam.240920.291120
UR - https://global-sci.org/intro/article_detail/eajam/18639.html
KW - Higher-order dispersive nonlinear Schrödinger equation, Riemann-Hilbert approach,
soliton solutions.
AB - <p style="text-align: justify;">The higher-order dispersive nonlinear Schrödinger equation with the zero
boundary conditions at the infinity is studied by the Riemann-Hilbert approach. We
consider the direct scattering problem, corresponding eigenfunctions, scattering matrix
and establish some of their properties. These results are used in the construction of an
associated Riemann-Hilbert problem. Assuming that the scattering coefficients possess
single or double poles, we derive the problem solutions. Finally, we present graphical
examples of 1-, 2- and 3-soliton solutions and discuss their propagation.</p>