论文标题
riemann-hilbert问题与光学和磁力机制中的四阶分散非线性schrödinger方程相关
Riemann-Hilbert problem associated with the fourth-order dispersive nonlinear Schrödinger equation in optics and magnetic mechanics
论文作者
论文摘要
在本文中，我们利用FOKAS方法来研究半行上的四阶分散非线性schrödinger（FODNLS）方程的初始边界价值问题（IBVP）铁磁链，具有八个杆和偶极相互作用。通过讨论lax对FODNL方程的本征函数和散射矩阵的分析和对称性，FODNLS方程的IBVPs表示为矩阵Riemann-Hilbert（RH）问题形式。然后，可以通过解决此矩阵RH问题来获取FODNLS方程的潜在函数解决方案$ u（x，t）$。此外，我们还获得了某些光谱功能可以接受关键的全球关系。
In this paper, we utilize Fokas method to investigate the initial-boundary value problems (IBVPs) of the fourth-order dispersive nonlinear Schrödinger (FODNLS) equation on the half-line, which can simulate the nonlinear transmission and interaction of ultrashort pulses in the high-speed optical fiber transmission system, and describe the nonlinear spin excitation phenomenon of one-dimensional Heisenberg ferromagnetic chain with eight poles and dipole interaction. By discussing the eigenfunctions of Lax pair of FODNLS equation and the analysis and symmetry of the scattering matrix, the IBVPs of FODNLS equation is expressed as a matrix Riemann-Hilbert (RH) problem form. Then one can get the potential function solution $u(x,t)$ of the FODNLS equation by solving this matrix RH problem. In addition, we also obtained that some spectral functions admits a key global relationship.
