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在逆散射方法下，求解了非局部非线性薛定谔方程在势为多场解时的线性特征值问题。与精确可解动力系统的关系从复平面上动力系统的角度研究了非局部NLS方程的周期解和孤子的极点运动。调制理论分析了非局部NLS方程周期解的调制问题。推导了波浪参数的调制方程，并对其进行了显式求解。初值问题的表述利用逆散射变换方法，给出了非局部NLS方程的初值问题。导出了约斯特函数的方程组。孤子解的新公式从非线性代数方程组中导出了Benjamin-Ono方程的多孤子解。这一结果是逆散射法方案所没有预料到的新发现

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 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。

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. 309(1-2). 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”《物理学快报》A.309(1-2)。

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。