Research of non-integrable systems by means of bilinear method

双线性法研究不可积系统

• 批准号: 11640121
• 负责人: ITO Masaaki
• 金额: $ 0.77万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640121/
• 关键词: Bilinear method; Non-integrable systems; Soliton; Modified Bessel function; Computer Algebra

We studied the discretization of differential equations to obtain the information of transformation between non-integrable differential equations and their bilinear forms. To this end, we completed the REDUCE program for finding analytic form of conserved densities of diference-difference equations. By using the program, we studied the stability of the model equation which has modified Bessel type potential, and confirm there exists nearly stable solitary wave solutions. The explicit bilinear form and the transformation of the model equation are now searching. In connection with conserved density of difference equations, we clarified the relation between the shift operator and the discrete Euler operator. Furthermore, a new approach for the study of the integrability of differential-difference systems is introduced. Each investigators of our research group achieved many accomplishment in their fields, and contributed to the progress of the present work.

研究了微分方程的离散化问题，得到了不可积微分方程与其双线性形式之间的转换信息。为此，我们完成了求解差分方程守恒密度解析形式的REDUCE程序。利用该程序研究了具有修正Bessel型势的模型方程的稳定性，证实了存在近稳定孤波解。模型方程的显式双线性形式和变换正在研究中。结合差分方程的守恒密度，阐明了移位算子与离散欧拉算子之间的关系。此外，还介绍了一种研究微分-差分系统可积性的新方法。本课题组的每一位研究者都在各自的领域取得了许多成就，为本课题的研究做出了贡献。

项目成果

M.Shiba: "Analytic continuation beyond the ideal boundary"Kokyuroku,Res.Inst.Math.sci.,Kyoto Univ.. 1155. 120-127 (2000)

M.Shiba：“超越理想边界的解析延续”Kokyuroku，Res.Inst.Math.sci.，京都大学. 1155. 120-127 (2000)

M.Shiba: "Ideal fluid flows on a noncompact Riemann surface and analytic continuation beyond the ideal boundary"Proc.the fourth Japan-Korea Workshop. 34-39 (2001)

M.Shiba：“非紧黎曼曲面上的理想流体流动和理想边界之外的解析延拓”，第四届日韩研讨会论文。

M.J.Ablowitz: "On Integrability and Chaos in Discrete Systems"Chaos, Solitons and Fractals. 11, No.1-3. 159-169 (2000)

M.J.Ablowitz：“论离散系统中的可积性和混沌”混沌、孤子和分形。

M.Shiba: "Analytic continuation beyond the ideal boundary"Real and Complex Analysis, Proc.the third Japan-Korea Workshop, Ewha Womans University, Seoul, Korea (ed.by S.Y.Lee). 26-35 (2000)

M.Shiba：“超越理想边界的分析延续”实数与复杂分析，第三届日韩研讨会，梨花女子大学，韩国首尔（S.Y.Lee 编辑）。

R.Willox: "Quadrilateral Lattices and Eigenfunction Potentials for N-component KP Hierarchies"Phys.Lett.A. 252. 163-172 (1999)

R.Willox：“N 分量 KP 层次结构的四边形格子和特征函数势”Phys.Lett.A。