论文标题
散射图决定了非线性
The scattering map determines the nonlinearity
论文作者
论文摘要
使用二维非线性schrödinger方程（NLS）作为模型示例，我们提出了一种从其小数据散射行为中恢复非线性分散方程的非线性的一般方法。我们证明，在对非线性的非常温和的假设下，波算子与散射图一样唯一地决定了非线性。评估对精心挑选的初始数据的散射图，我们将问题减少到反向卷积问题，我们通过应用Beurling-Lax定理来解决该问题。
Using the two-dimensional nonlinear Schrödinger equation (NLS) as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild assumptions on the nonlinearity, the wave operator uniquely determines the nonlinearity, as does the scattering map. Evaluating the scattering map on well-chosen initial data, we reduce the problem to an inverse convolution problem, which we solve by means of an application of the Beurling--Lax Theorem.
