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Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles

Advances in Applied Mathematics and Mechanics, 2022
We employ the Riemann-Hilbert (RH) method to study the Hirota equation with arbitrary order zero poles under zero boundary conditions. Through the spectral analysis, the asymptoticity, symmetry, and analysis of the Jost functions are obtained, which play
Xiaofan Zhang, S. null, Jin-Jie Yang
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The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrodinger Systems on the Half-Line

East Asian Journal on Applied Mathematics, 2018
An integrable coherently coupled nonlinear Schrödinger system describing the propagation of polarised optical waves in an isotropic medium with a generalized 4 × 4 matrix Ablowitz-Kaup-Newell-Segur-type Lax pair is studied.
Beibei Hu
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THE mKdV EQUATION ON THE HALF-LINE

Journal of the Institute of Mathematics of Jussieu, 2004
A. B. D. Monvel, A. Fokas, D. Shepelsky
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