The direct and inverse scattering problem for the semilinear Schrodinger equation
The direct and inverse scattering problem for the semilinear Schrodinger equation
复制标题
半线性薛定谔方程的正散射和逆散射问题
DOI：
10.1007/s00030-020-00627-x
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Takashi Furuya
中科院分区：
文献类型：
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作者：
Tomohiro Daimona;Takashi Furuya and Ryuji Saiina;Takashi Furuya
研究了半线性Schrödinger方程的正散射和逆散射问题。利用Banach不动点定理证明了直接问题小解的适定性，且解在无穷远处具有一定的渐近性。我们还证明了反问题，即半线性函数（x,z）是由散射振幅唯一确定的。其思想是线性化通过使用具有多个参数的源我们对非线性方程对这些参数进行微分以得到线性方程。
We study the direct and inverse scattering problem for the semilinear Schrödinger equationin. We show well-posedness in the direct problem for small solutions based on the Banach fixed point theorem, and the solution has the certain asymptotic behavior at infinity. We also show the inverse problem that the semilinear functiona(x,z) is uniquely determined from the scattering amplitude. The idea is the linearization that by using sources with several parameters we differentiate the nonlinear equation with respect to these parameter in order to get the linear one.