标题： 关于离散Hirota方程具有非零边界条件的逆散射变换 显示英文标题

标题： On the inverse scattering transform to the discrete Hirota equation with nonzero boundary conditions

摘要： 本研究调查了具有非零边界条件的离散 Hirota 方程的鲁棒逆散射变换，该变换用于同时求解分支点上的任意阶极点和光谱奇异性。 利用逆散射变换方法，我们构建了达布变换，但没有采用极限过程，这比以往的方法更为方便。 详细推导了几类有理解。 这些解包括 W 形孤子、呼吸子、高阶 rogue 波以及孤子与呼吸子之间的各种相互作用。 此外，我们通过图形分析了有理解的一些显著特征。 我们的结果有助于解释相关的非线性波现象。 显示英文摘要

摘要： Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral singularities. Using the inverse scattering transform method, we construct the Darboux transformation but not with the limit progress, which is more convenient than before. Several kinds of rational solutions are derived in detail. These solutions contain W-shape solitons, breathers, high-order rogue waves, and various interactions between solitons and breathers. Moreover, we analyze some remarkable characteristics of rational solutions through graphics. Our results are useful to explain the related nonlinear wave phenomena.