Study on the asymptotic behavior of solutions for the nonlocal soliton equations in the zero dispersion limit

非局部孤子方程零色散极限解的渐近行为研究

• 批准号: 16540196
• 负责人: MATSUNO Yoshimasa
• 金额: $ 2.3万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540196/
• 关键词: Soliton; Nonlinear wave equation; Zero dispersion limit; Camassa-Holm equation; Degasperis-Procesi equation; Benjamin-Ono equation; Inverse scattering method; Peakon solution

1.New representation of the solutions for the nonlocal soliton equationsNew representations are obtained for the soliton and peiodic-wave solutions of the Benjamin-Ono and nonlocal nonlinear Schrodinger equations. Their derivation is based on a system of nonlinear algebraic equations. The method used here differs from the corresponding derivation by means of the inverse scattering method.2.Parametric representation of the multisoliton solution for the Camassa-Holm equationThe multisoliton solution (N-soliton solution) of the Camassa-Holm (CH) equation is constructed by means of the Hodograph transformation. Unlike the usual representation for the soliton solutions, it has a parametric representation. The large time asymptotic of the solution is derived and the formula for the phase shift is obtained.3.Multisoliton solutions of the Degasperis-Procesi equation and their peakon limitUsing the procedure similar to that used for the CH equation, the one- and two-soliton solutions of the Degaspeis-Procesi (DP) equation are constructed and their properties are explored in detail. A remarkable feature of the one-soliton solution is that the amplitude depends on its velocity nonlinearly. The peakon solution is reduced from the soliton solution by taking the zero dispersion limit. The asymptotic form of the two-soliton solution is also derived together with the associated formula for the phase shift. In a subsequent study, the general N-soliton solution is obtained for the DP equation and its property is examined.

1.对于本杰明蛋白 - 单位和非局部非线性非线性schrodinger方程的孤子和peiodic波溶液，获得了非局部孤子方程式New表示溶液的新溶液。它们的推导基于非线性代数方程系统。此处使用的方法与相应的衍生方法通过逆散射方法不同。2。Camassa-Holm方程的MultiSoliton溶液的参数表示，Camassa-Holm（CH）方程的Multisoliton溶液（N-SOLITON溶液）是通过Hoshodographsoptry Transformation构建的。与孤子解决方案的通常表示不同，它具有参数表示。得出了溶液的较大时间渐近性，并获得了相移的公式。3.Degasperis-Procosi方程及其peamon的多菌液解决方案限制了与CH方程相似的过程，单一和两索子溶液的degaspeis-procesi（dp）平等溶液构建了属性，并构建了属性。单索顿解决方案的一个显着特征是振幅非线性取决于其速度。通过取零色散极限，从孤子溶液中降低了峰溶液。两索溶液的渐近形式也与相关的相关公式一起得出。在随后的研究中，获得了DP方程的一般N-Soliton解决方案，并检查了其性质。

项目成果

Intermediate value theorem for functions on classes of Riemann surfaces

黎曼曲面类上函数的中值定理

• 发表时间: 2005
• 期刊: Geometric Function Theory in Several Complex Variables (掲載予定)
• 作者: Jun-ichi Inoguchi;Kenji Kuwabara;Hiroo Naitoh;Katsuhiro Komiya;Hiroo Naitoh;Katsuhiro Komiya;Makoto Masumoto
• 通讯作者: Makoto Masumoto

Free boundary problem for one-dimensional motions of compressible gas and vacuum

• DOI: 10.1007/bf03167467
• 发表时间: 2004-06
• 期刊: Japan Journal of Industrial and Applied Mathematics
• 影响因子: 0.9
• 作者: Mari Okada

Circularizable domains on Riemann surfaces

黎曼曲面上的可圆化域

• 发表时间: 2005
• 期刊: Kodai Math. J. 28
• 作者: M. Masumoto;and M. Shiba
• 通讯作者: and M. Shiba

New representation of multiperiodic and multisoliton solutions for a class of nonlocal soliton equations

一类非局部孤子方程多周期和多孤子解的新表示

• 发表时间: 2004
• 期刊: Journal of the Physical Society of Japan 73(12)
• 作者: S.-U.Ryu;A.Yagi;Y.Goto;F.Kobayashi;M.Efendiev;J-H.Ha;Y.Matsuno;S.Haruki;Y.Naito;Y.Matsuno;Y.Naito;F.Kojima;Y.Matsuno;Y.Matsuno
• 通讯作者: Y.Matsuno

New representation of multiperiodic and multisoliton solution for a class of nonlocal soliton equations

一类非局部孤子方程多周期多孤子解的新表示

• 发表时间: 2004
• 期刊: Journal of the Physical Society of Japan Vol.73
• 作者: S.-U.Ryu;A.Yagi;Y.Goto;F.Kobayashi;M.Efendiev;J-H.Ha;Y.Matsuno;S.Haruki;Y.Naito;Y.Matsuno
• 通讯作者: Y.Matsuno