TY - JOUR
T1 - Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method
AU - Wang , Guixian
AU - Wang , Xiu-Bin
AU - Han , Bo
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 260
EP - 280
PY - 2024
DA - 2024/04
SN - 14
DO - http://doi.org/10.4208/eajam.2023-001.030523 
UR - https://global-sci.org/intro/article_detail/eajam/23062.html
KW - Hirota equation, inverse scattering method, Riemann-Hilbert problem, multiple pole solution.
AB - <p style="text-align: justify;">In this paper, we study multiple pole solutions for the focusing Hirota equation under the nonzero boundary conditions via inverse scattering method. The direct
scattering problem is based on the spectral analysis and exhibits the Jost solutions, scattering matrix as well as their analyticity, symmetries and asymptotic behaviors. Compared with previous studies, we define a more complex discrete spectrum. The inverse
scattering problem is explored by solving the corresponding matrix Riemann-Hilbert
problems. Particularly, we solve the scattering problem by a suitable uniformization
variable on the complex $z$-plane instead of a two-sheeted Riemann surface. Finally, we
deduce general formulas of $N$-double pole and $N$-triple pole solutions with mixed discrete spectra and show some prominent characteristics of these solutions graphically. Our
results should be helpful to further explore and enrich breather wave phenomena arising
in nonlinear and complex systems.</p>