论文标题
分数集成和相关的离散非线性schrödinger方程
Fractional Integrable and Related Discrete Nonlinear Schrödinger Equations
论文作者
论文摘要
可集成的分数方程，例如分数Korteweg-devries和非线性schrödinger方程是非线性动力学和分数计算的相交的关键。在此手稿中，发现了这种类型的第一个离散/微分差方程，即可分数的离散非线性schrödinger方程。该方程式是线性化的；发现特殊的孤子溶液的峰值速度比其他先前获得的分数集成方程更为复杂。将该方程与密切相关的分数平均离散非线性schrödinger方程进行比较，该方程的结构比可集成的情况更简单。对于正分数参数和小振幅波，可集成和平均方程的孤子解具有相似的行为。
Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schrödinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential difference equation of this type is found, the fractional integrable discrete nonlinear Schrödinger equation. This equation is linearized; special soliton solutions are found whose peak velocities exhibit more complicated behavior than other previously obtained fractional integrable equations. This equation is compared with the closely related fractional averaged discrete nonlinear Schrödinger equation which has simpler structure than the integrable case. For positive fractional parameter and small amplitude waves, the soliton solutions of the integrable and averaged equations have similar behavior.
