We study the Cauchy problem of the focusing Hirota equation with fastly decay initial value at infinity via Riemann-Hilbert (RH) approach. The Jost function and scattering matrix related to the initial value are obtained by spectral analysis, and their analytical, asymptotic and symmetric properties are analyzed. The solution of the Hirota equation is derived by solving the corresponding RH problem, which contains two cases of scattering data with single zeros and double zeros. The general form of solutions with no reflection potential is obtained. The two types of the discrete spectrum are selected for the purpose of comparing the influence of different eigenvalues on solution propagation behavior.

我们通过Riemann-Hilbert（RH）方法研究了无限远处具有快速衰减初始值的聚焦Hirota方程的Cauchy问题。通过光谱分析获得与初始值相关的Jost函数和散射矩阵，并对它们的解析，渐近和对称性质进行分析。Hirota方程的解是通过求解相应的RH问题得出的，该问题包含两种情况，即散射数据具有单零和双零的情况。获得了没有反射电势的溶液的一般形式。选择两种类型的离散频谱是为了比较不同特征值对溶液传播行为的影响。