论文标题
通用双曲线诺维科夫 - 韦斯特洛夫方程的库奇问题通过木马对称性
The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation via the Moutard symmetries
论文作者
论文摘要
首先，我们引入了一个新的程序，用于构建基于Moutard Symmetry的实用值（双曲）Novikov-Veselov方程的Cauchy问题。其中显示的过程利用了众所周知的通风函数$ \ ai（ξ）$，这反过来又是对普通微分方程$ \ frac {d^2 z} {dξ^2} =ξz$的解决方案。在本文的第二部分中，我们表明，上述过程也可以适用于Novikov-veselov方程的$ n $ ther订单概括，但前提是一个可以用普通微分方程$ \ frac {d^{n-1} Z} Z} Z} Z} Z} {D^n-demed^n-d emed^{n-1 n-1} {n-1}}的适当解决方案代替通风函数。
We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov-Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function $\Ai(ξ)$ which in turn serves as a solution to the ordinary differential equation $\frac{d^2 z}{d ξ^2} = ξz$. In the second part of the article we show that the aforementioned procedure can also work for the $n$-th order generalizations of the Novikov-Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation $\frac{d^{n-1} z}{d ξ^{n-1}} = ξz$.
