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 equationwith arbitrary order zero poles under zero boundary conditions. Through the spectralanalysis, the asymptoticity, symmetry, and analysis of the Jost functions are obtained,which play a key role in constructing the RH problem. Then we successfully established the exact solution of the equation without reflection potential by solving the RHproblem. Choosing some appropriate parameters of the resulting solutions, we furtherderive the soliton solutions with different order poles, including four cases of a fourth-order pole, two second-order poles, a third-order pole and a first-order pole, and fourfirst-order points. Finally, the dynamical behavior of these solutions are analyzed viagraphic analysis.