论文标题
对聚焦非线性Schrodinger方程的逆散射变换，并反向传播流
Inverse scattering transform for the focusing nonlinear Schrodinger equation with counterpropagating flows
论文作者
论文摘要
针对聚焦非线性Schrodinger方程的逆散射变换是针对一类初始条件类别的一类，其无穷大的渐近行为由反向传播波组成。该公式考虑了相关散射问题的两个渐近特征值的分支性质。 jost本征函数和散射系数被明确定义为复杂平面上的单值函数，并沿着某些分支切割，跳跃不连续性。明确讨论了分支点的分析性能，对称性，离散频谱，渐近性和行为。逆问题被提出为矩阵riemann-hilbert的问题。明确讨论了对文献中先前讨论的所有案例的减少。明确计算了与几种由与物理相关的Riemann问题组成的特殊情况相关的散射数据。
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into account the branched nature of the two asymptotic eigenvalues of the associated scattering problem. The Jost eigenfunctions and scattering coefficients are defined explicitly as single-valued functions on the complex plane with jump discontinuities along certain branch cuts. The analyticity properties, symmetries, discrete spectrum, asymptotics and behavior at the branch points are discussed explicitly. The inverse problem is formulated as a matrix Riemann-Hilbert problem with poles. Reductions to all cases previously discussed in the literature are explicitly discussed. The scattering data associated to a few special cases consisting of physically relevant Riemann problems are explicitly computed.
