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.非局域孤子方程解的新表示形式获得了Benjamin-Ono和非局域非线性薛定谔方程的孤子解和周期波解的新表示形式。它们的推导基于非线性代数方程组。这里使用的方法与相应的逆散射法推导不同。2.Camassa-Holm方程多孤子解的参数化表示Camassa-Holm(CH)方程的多孤子解(N-孤子解)的构造通过 Hodograph 变换。与孤子解的通常表示不同，它具有参数表示。推导了该解的大时间渐近性，并得到了相移的公式。 3. Degasperis-Procesi 方程的多孤子解及其峰值极限 使用与 CH 方程类似的过程，可以得到一阶和二阶解构造了 Degaspeis-Procesi (DP) 方程的孤子解，并详细探讨了它们的性质。单孤子解的一个显着特征是振幅非线性地取决于其速度。通过取零色散极限，将孤子解简化为峰值解。还导出了双孤子解的渐近形式以及相移的相关公式。在随后的研究中，获得了DP方程的一般N-孤子解并检验了其性质。

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