论文标题
局部和非局部非共同第四阶五级非线性schrodinger方程的整合性
Integrability of local and nonlocal non-commutative fourth order quintic nonlinear Schrodinger equations
论文作者
论文摘要
我们证明了广义的非交通性第四阶非线性schrodinger方程的整合性。证明相对简洁，并植根于由CH开创的线性化方法。 poppe。它基于求解相应的线性偏差系统，以生成“散射数据”的进化Hankel操作员。然后，通过求解与Marchenko方程相对应的线性Fredholm方程来生成非共同非线性偏差系统的时间进化解决方案。从Ablowitz和Musslimani的意义上讲，反向时空和反向时间非本地版本的整合性在第四阶非线性非线性Schrodinger方程式是通过所采用的方法的连续性证明的。此外，我们基于上面的分析方法实施了数值集成方案，该方案涉及求解线性偏差系统，然后数值求解线性fredholm方程以在任何给定时间生成解决方案。
We prove integrability of a generalised non-commutative fourth order quintic nonlinear Schrodinger equation. The proof is relatively succinct and rooted in the linearisation method pioneered by Ch. Poppe. It is based on solving the corresponding linearised partial differential system to generate an evolutionary Hankel operator for the `scattering data'. The time-evolutionary solution to the non-commutative nonlinear partial differential system is then generated by solving a linear Fredholm equation which corresponds to the Marchenko equation. The integrability of reverse space-time and reverse time nonlocal versions, in the sense of Ablowitz and Musslimani, of the fourth order quintic nonlinear Schrodinger equation are proved contiguously by the approach adopted. Further, we implement a numerical integration scheme based on the analytical approach above which involves solving the linearised partial differential system followed by numerically solving the linear Fredholm equation to generate the solution at any given time.
