非零边界条件下离散Hirota方程的反散射变换研究  

On the Inverse Scattering Transform to the Discrete Hirota Equation with Nonzero Boundary Conditions

作　　者：王贵贤 王秀彬 韩波[3] GuiXianWANG;XiuBin WANG;Bo HAN(School of Science,Jiangsu University of Science and Technology,Zhenjiang 212100,P.R.China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,P.R.China;School of Mathematics,Harbin Institute of Technology,Harbin 150001,P.R.China)

机构地区：[1]江苏科技大学理学院,镇江212100 [2]中国矿业大学数学学院,徐州221116 [3]哈尔滨工业大学数学学院,哈尔滨150001

出　　处：《数学学报（中文版）》2024年第6期1049-1076,共28页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12271129,12201622);国家留学基金委资助项目(202206120152)。

摘　　要：本文利用反散射变换法探索了具有非零边界条件的离散Hirota方程,同时求解了分支点和谱奇异点上的任意阶极点.基于鲁棒反散射变换构造的Darboux矩阵,相较于现存研究成果,避免了对谱参数极限处理步骤,从而简化了计算过程.最终详细推导了几种有理解的紧化表达式,其中包含W-型孤子、呼吸波、以及高阶怪波解.并且通过绘制三维图和沿空间分量波的传播图,形象地展示了上述解的显著特征,此外,它们之间的相互作用也可直观地观察到.研究结果有助于解释相关的非线性波动现象,进而揭示其产生原理与机制.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 Wshape 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.

关 键 词：离散Hirota方程 反散射变换法 RIEMANN-HILBERT问题 DARBOUX变换 

分 类 号：O175.2[理学—数学]