论文标题
非局部非线性非线性Schrodinger方程的散落的理性解决方案：渐近分析和孤子相互作用
Rational solutions of the defocusing nonlocal nonlinear Schrodinger equation: Asymptotic analysis and soliton interactions
论文作者
论文摘要
在本文中，我们获得了通过Darboux转换和某些极限技术来散入非局部非线性Schrodinger方程的N级合理解决方案。然后，通过改进的渐近分析方法，依靠不同代数项之间的平衡，我们通过1 <= n <= 4的顺序得出了有理解的所有渐近孤子的显式表达。事实证明，渐近孤子位于直曲线或代数曲线中，精确的溶液接近弯曲的渐近孤子，其速率速度较慢。此外，我们发现所有理性解决方案仅表现出五种不同类型的孤子相互作用，而相互作用的孤子则分为两半，每半都具有相同的幅度。特别是对于弯曲的渐近孤子，在T和-T之间，在某些参数条件下，它们之间的速度可能会略有差异。此外，我们揭示了与N> = 2的有理解中的孤子相互作用比指数和指数和理性的解决方案中的孤子相互作用强。
In this paper, we obtain the Nth-order rational solutions for the defocusing nonlocal nonlinear Schrodinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1<=N<=4. It turns out that the asymptotic solitons are localized in the straight or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and -t with certain parametric condition. In addition, we reveal that the soliton interactions in the rational solutions with N>=2 are stronger than those in the exponential and exponential-and-rational solutions.
