Study on the behavior of solutions in the zero dispersion limit of the nonlinear wave equations with the integral kernel

带积分核的非线性波动方程零色散极限解的行为研究

• 批准号: 14540209
• 负责人: MATSUNO Yoshimasa
• 金额: $ 2.24万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540209/
• 关键词: nonlinear wave equation; soliton; modulation theory; zero dispersion limit; inverse scattering method; Benjamin-Ono equation; nonlocal nonlinear Schrodinger equation

1. Exactly solvable eigenvalue problemThe linear eigenvalue problem is solved for the nonlocal nolonear Schrodinger (NLS) equation in the context of the inverse scattering method when the potential is the multisolison solution2. Relation to exactly solvable dynamical systemsThe motion of poles of the soliton and periodic solutions of the nonlocal NLS equation is investigated from the viewpoint of the dynamical system in the complex plane3. Modulation theoryThe modulation problem is analyzed for the periodic solution of the nonlocal NLS equation. The modulation equations for the wave parameters are derived and they are solved explicitly4. Formulation of the initial value problemThe initial value problem of the nonlocal NLS equation is formulated by means of the inverse scattering transform method. A system of equations are derived for the Jost functions5. New formula for the soliton solutionThe multisoliton solution of the Benjamin-Ono equation is derived from a system of nonlinear algebraic equations. This result is a new finding which is never anticipated from the scheme of the inverse scattering method

1. 精确可解的特征值问题 当势为多孤点解时，在逆散射方法的背景下，求解非局部非孤薛定谔 (NLS) 方程的线性特征值问题2。与精确可解动力系统的关系从复平面动力系统的角度研究了孤子极点的运动和非局部 NLS 方程的周期解。调制理论分析了非局部NLS方程周期解的调制问题。导出了波参数的调制方程并对其进行了显式求解4。初值问题的表述非局部NLS方程的初值问题是通过逆散射变换方法来表述的。推导出约斯特函数的方程组5。孤子解的新公式Benjamin-Ono 方程的多孤子解是从非线性代数方程组导出的。这个结果是逆散射方法方案中从未预料到的新发现

项目成果

T.Makino: "Approximations of relativistic Euler-Poisson-Darboux equation"Funkcialaj Ekvacioj. 46. 23-45 (2003)

T.Makino：“相对论 Euler-Poisson-Darboux 方程的近似”Funkcialaj Ekvacioj。

Y.Matsuno: "Asymptotic solutions of the nonlocal nonlinear Schrodmger equation in the limit of small dispersion"Physics Letters A. 309(1-2). 83-89 (2003)

Y.Matsuno：“小色散极限下非局部非线性薛姆格方程的渐近解”《物理学快报》A. 309(1-2)。

Y.Matsuno: "Asymptotic solutions of the nonlocal nonlinear Schrodinger equation in the limit of small dispersion"Physics Letters A. Vol.309. 83-89 (2003)

Y.Matsuno：“小色散极限下非局部非线性薛定谔方程的渐近解”《物理快报》A. Vol.309。

S.Furuichi, K.Yanagi, K.Kuriyama: "A sufficient condition on concavity of the auxiliary function appearingin quantum reliability function"INFORMATION. 6. 71-76 (2003)

S.Furuichi、K.Yanagi、K.Kuriyama：“量子可靠性函数中出现的辅助函数凹性的充分条件”信息。

T.Makino: "Approximation of he Relativistic Euler-Poisson-Darboux Equation"Funkcialaj Ekvacioj. 46. 23-45 (2003)

T.Makino：“相对论 Euler-Poisson-Darboux 方程的近似”Funkcialaj Ekvacioj。