论文标题
用于扩展的非线性schrödinger方程的高级孤子矩阵
High-order soliton matrix for an extended nonlinear Schrödinger equation
论文作者
论文摘要
具有三阶项和四阶项的扩展非线性schrödinger（ENLS）方程，描述了光纤中的波传播比NLS方程更准确。对Riemann-Hilbert问题（RHP）框架中的ENLS方程提出了高阶孤子基质的研究。通过标准的敷料程序和广义的Darboux转换（GDT），用于ENLS方程的RHP中的简单零和基本高阶零的Soliton矩阵。然后可以确定ENRS方程的N-溶液和高阶孤子溶液。此外，对碰撞动力学以及两丝岩的渐近行为以及高阶一soliton的长期渐近估计进行了具体分析。对于给定的光谱参数，我们可以通过调整ENER方程的自由参数来控制传播方向，速度，宽度和其他物理量。
The extended nonlinear Schrödinger (ENLS) equation with third-order term and fourth-order term which describes the wave propagation in the optical fibers is more accurate than the NLS equation. A study of high-order soliton matrix is presented for an ENLS equation in the framework of the Riemann-Hilbert problem (RHP). Through a standard dressing procedure and the generalized Darboux transformation (gDT), soliton matrix for simple zeros and elementary high-order zeros in the RHP for the ENLS equation are constructed. Then the N-soliton solutions and high-order soliton solutions for the ENLS equation can be determined. Moreover, collision dynamics along with the asymptotic behavior for the two-solitons and long-time asymptotic estimations for the high-order one-soliton are concretely analyzed. For the given spectral parameters, we can control the propagation direction, velocity, width and other physical quantities of solitons by adjusting the free parameters of ENLS equation.
