Multidimensional Inverse Scattering for the Nonlinear Klein-Gordon Equation with a Potential
Multidimensional Inverse Scattering for the Nonlinear Klein-Gordon Equation with a Potential
复制标题
具有势的非线性Klein-Gordon方程的多维逆散射
DOI：
10.1006/jdeq.2001.4133
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发表时间：
2002
影响因子：
2.4
通讯作者：
R. Weder
中科院分区：
文献类型：
--
作者：
R. Weder
在本文中，我们求解Rn,n⩾2:∂2∂t2u(x,t)−Δu(x,t)+u(x,t)+V0(x)u(x,t)+Σj=1∞Vj(x)∣u∣2(j0+j)u(x,t)=0上的非线性Klein-Gordon方程的多维逆散射问题。我们证明了散射算子的小幅度极限唯一地决定了所有的Vj,j=0,1,…。我们的证明还给出了一种重建 Vj,j=0,1,… 的方法。
In this paper, we solve the multidimensional inverse scattering problem for the nonlinear Klein–Gordon equation on Rn,n⩾2:∂2∂t2u(x,t)−Δu(x,t)+u(x,t)+V0(x)u(x,t)+∑j=1∞Vj(x)∣u∣2(j0+j)u(x,t)=0. We prove that the small-amplitude limit of the scattering operator determines uniquely all the Vj,j=0,1,…. Our proof gives, as well, a method for the reconstruction of the Vj,j=0,1,….