论文标题
用于解决非线性Schroedinger方程系统的光谱散射问题的有效算法
Efficient algorithms for solving the spectral scattering problems\\ for the Manakov system of nonlinear Schroedinger equations
论文作者
论文摘要
提出了``矢量''的数值算法，以解决非线性矢量schroedinger方程的逆和直接光谱散射问题，并考虑到波浪极化，称为马纳科夫系统。结果表明，由特殊矢量样矩阵组成的新的4块矩阵组成的新代数组使标量问题的数值算法的概括性成为可能对向量案例的数值算法的概括，无论是用于焦点和defocing Manakov Systems。与标量情况一样，反向散射问题的解决方案包括使用Levinson类型的Toeplitz内部边框算法的Gelfand-Levitan-Marchenko积分方程的离散系统的矩阵倒置。也类似于标量案例，用于解决通过反向散射问题的算法步骤获得的直接散射问题的算法。通过将计算结果与已知的精确分析解决方案（Manakov Vector soliton）进行比较，对矢量算法的测试证实了矢量算法的数值效率。
``Vectorial'' numerical algorithms are proposed for solving the inverse and direct spectral scattering problems for the nonlinear vector Schroedinger equation, taking into account wave polarization, known as the Manakov system. It is shown that a new algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices makes possible the generalization of numerical algorithms of the scalar problem to the vector case, both for the focusing and defocusing Manakov systems. As in the scalar case, the solution of the inverse scattering problem consists of inversion of matrices of the discretized system of Gelfand-Levitan-Marchenko integral equations using the Toeplitz Inner Bordering algorithm of Levinson's type. Also similar to the scalar case, the algorithm for solving the direct scattering problem obtained by inversion of steps of the algorithm for the inverse scattering problem. Testing of the vector algorithms performed by comparing the results of the calculations with the known exact analytical solution (the Manakov vector soliton) confirmed the numerical efficiency of the vector algorithms.
