Multiple Pole Solutions of the Hirota Equation Under Nonzero Boundary Conditions by Inverse Scattering Method
Year: 2024
Author: Guixian Wang, Xiu-Bin Wang, Bo Han
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 2 : pp. 260–280
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-001.030523
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 2 : pp. 260–280
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Hirota equation inverse scattering method Riemann-Hilbert problem multiple pole solution.