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本杰明-奥诺方程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。它们的推导是基于一组非线性代数方程。2.Camassa-Holm方程多孤子解的参数表示通过Hodoggraph变换构造了Camassa-Holm(CH)方程的多孤子解(N-孤子解)。与通常的孤子解表示法不同，它有一个参数表示法。3.DeGasperis-Procesi方程的多孤子解及其峰值极限用类似于CH方程的方法，构造了Degaspeis-Procesi(DP)方程的单孤子解和双孤子解，并详细讨论了它们的性质。单孤子解的一个显着特点是其振幅与其速度成非线性关系。通过取零色散极限，峰子解由孤子解简化为孤子解。导出了双孤子解的渐近形式，并给出了相应的相移公式。在随后的研究中，得到了DP方程的一般N-孤子解，并考察了它的性质。

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

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

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

A relaxation method for constructing a Beltrami flow in a bounded domain

有界域内构造贝尔特拉米流的松弛方法

• 发表时间: 2005
• 期刊: J.Math.Phys. 46・8
• 作者: Akira SASAMOTO;Takayuki SUZUKI;Yoshihiro NISHIMURA;海津聰;藤間 昌一;笹本 明;Satoshi Kaizu;笹本明;川添良幸;Takahito Nishiyama;Takahiro Nishiyama;Takahiro Nishiyama;後藤 ミドリ;Takahiro Nishiyama;西原 賢;西山 高弘
• 通讯作者: 西山 高弘

A Cauchy problem for the nonlocal nonlinear Schrodinger equation

非局部非线性薛定谔方程的柯西问题

• 发表时间: 2004
• 期刊: Inverse Problems 20
• 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
• 通讯作者: Y.Matsuno