Dunajski方程的精确解及其线性系统的长时间演化性
发布时间：2019-05-24 12:53
【摘要】：反散射作为重要的数学物理方法,主要用于研究非线性可积偏微分方程.2005年,Manakov和Santini提出了一种新的反散射方法,通过研究与单参数向量场形式的Lax对相联系的正问题和反问题,求解流体力学型非线性可积偏微分方程.本文主要基于这种新的反散射方法讨论(3+1)维的Dunajski方程的精确解.该方程与来源于Einstein(反)自对偶引力场方程,在数学和物理中具有重要的研究意义.本文通过构造与双曲函数有关的可解非线性Riemann-Hilbert问题,以及通过动力系统来构造满足条件的非线性Riemann-Hilbert问题来研究Dunajski方程的解,同时考虑线性化的Dunajski方程的解的长时间演化性。
[Abstract]:Backscattering, as an important mathematical and physical method, is mainly used to study nonlinear integrable partial differential equations. In 2005, Manakov and Santini proposed a new backscattering method. By studying the positive and inverse problems related to Lax pairs in the form of single parameter vector fields, the nonlinear integrable partial differential equations of fluid mechanics are solved. In this paper, the exact solution of (31) dimensional Dunajski equation is discussed based on this new backscattering method. The equation and the equation derived from Einstein (inverse) self-dual gravitational field are of great significance in mathematics and physics. In this paper, the solution of Dunajski equation is studied by constructing the solvable nonlinear Riemann-Hilbert problem related to hyperbolic function and constructing the nonlinear Riemann-Hilbert problem satisfying the condition by dynamic system. At the same time, the long time evolution of the solution of the linear Dunajski equation is considered.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2484875
[Abstract]:Backscattering, as an important mathematical and physical method, is mainly used to study nonlinear integrable partial differential equations. In 2005, Manakov and Santini proposed a new backscattering method. By studying the positive and inverse problems related to Lax pairs in the form of single parameter vector fields, the nonlinear integrable partial differential equations of fluid mechanics are solved. In this paper, the exact solution of (31) dimensional Dunajski equation is discussed based on this new backscattering method. The equation and the equation derived from Einstein (inverse) self-dual gravitational field are of great significance in mathematics and physics. In this paper, the solution of Dunajski equation is studied by constructing the solvable nonlinear Riemann-Hilbert problem related to hyperbolic function and constructing the nonlinear Riemann-Hilbert problem satisfying the condition by dynamic system. At the same time, the long time evolution of the solution of the linear Dunajski equation is considered.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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相关硕士学位论文 前1条
1 郭吉刚;Dunajski方程的精确解及其线性系统的长时间演化性[D];华侨大学;2017年
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