论文标题
准线性动力学{Ö} dinger方程的时间相关系数的重建
Reconstruction for the time-dependent coefficients of a quasilinear dynamical Schr{ö}dinger equation
论文作者
论文摘要
我们研究了与$ \ rb^n，n \ geq 2 $的有界域中的动态schr {Ö}方程相关的反问题。由于相关的非线性Schrödinger方程具有微不足道的解决方案，因此我们将微不足道溶液周围的方程线性化。在适当条件下，在初始和边界数据上证明了直接问题的适当性，可以观察到该解决方案允许$ \ eps $ - expansion。 By taking into account the fact that the terms $\Oh(|\nabla u(t,x)|^3)$ are negligible in this context, we shall reconstruct the time-dependent coefficients such as electric potential and vector-valued function associated with quadratic nonlinearity from the knowledge of input-output map using the geometric optics solution and Fourier inversion.
We study an inverse problem related to the dynamical Schr{ö}dinger equation in a bounded domain of $\Rb^n,n\geq 2$. Since the concerned non-linear Schrödinger equation possesses a trivial solution, we linearize the equation around the trivial solution. Demonstrating the well-posedness of the direct problem under appropriate conditions on initial and boundary data, it is observed that the solution admits $\eps$-expansion. By taking into account the fact that the terms $\Oh(|\nabla u(t,x)|^3)$ are negligible in this context, we shall reconstruct the time-dependent coefficients such as electric potential and vector-valued function associated with quadratic nonlinearity from the knowledge of input-output map using the geometric optics solution and Fourier inversion.
