| 张泽璇,张建兵.一个与Toda格相关的微分差分方程族及其反散射变换[J].数学研究及应用,2022,42(1):57~72 |
| 一个与Toda格相关的微分差分方程族及其反散射变换 |
| A Differential-Difference Hierarchy Related to the Toda Lattice and Its Inverse Scattering Transformation |
| 投稿时间：2020-11-13 修订日期：2021-01-28 |
| DOI：10.3770/j.issn:2095-2651.2022.01.006 |
| 中文关键词: Toda格 反散射变换 孤子解 |
| 英文关键词:Toda lattice inverse scattering transformation soliton solution |
| 基金项目:国家自然科学基金(Grant Nos.11101350; 11671177; 11771186), 江苏省研究生科研与实践创新计划(Grant No.KYCX21_2566). |
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| 中文摘要: |
| 通过组合谱参数的幂发展规律和积分初值常数,一个新的微分差分方程族从Toda格谱问题中导出.作为约束的特例,这个方程族包含了经典的Toda格方程、非等谱Toda格方程及混合的Toda格方程.详细分析了反散射变换中散射数据的演化,并通过这个方法获得了该方程族的精确解. |
| 英文摘要: |
| By combined power evolution laws of the spectral parameter λ and the initial constants of integration, a new differential-difference hierarchy is presented from the Toda spectral problem. The hierarchy contains the classic Toda lattice equation, the nonisospectral Toda lattice equation and the mixed Toda lattice equation as reduced cases. The evolution of the scattering data in the inverse scattering transform is analyzed in detail and exact soliton solutions are computed through the corresponding inverse scattering transform. |
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