论文标题
分数N-丝元溶液的动力学，具有可集成的分数高阶非线性schrödinger方程的异常分散体的动力学
Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations
论文作者
论文摘要
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrodinger (fHONLS) equations, containing the fractional Hirota (fHirota), fractional complex mKdV (fcmKdV), and fractional Lakshmanan-Porsezian-Daniel (fLPD)方程等。反向散射问题可以通过简单的杆子的矩阵riemann-hilbert问题来精确解决。结果，在无反射情况下FHONLS方程的分数N-溶液溶液中发现了明确的公式。特别是，我们分析了Fhirota和FCMKDV方程异常分散的分数单，两和三核溶液。这些包膜分数1-Soliton溶液的波，组和相速度与其振幅的功率定律有关。这些获得的分数n-丝状溶液可能有助于解释分数非线性培养基中非线性波的相关超分散转运。
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrodinger (fHONLS) equations, containing the fractional Hirota (fHirota), fractional complex mKdV (fcmKdV), and fractional Lakshmanan-Porsezian-Daniel (fLPD) equations, etc. The inverse scattering problem can be solved exactly by means of the matrix Riemann-Hilbert problem with simple poles. As a consequence, an explicit formula is found for the fractional N-soliton solutions of the fHONLS equations in the reflectionless case. In particular, we analyze the fractional one-, two- and three-soliton solutions with anomalous dispersions of fHirota and fcmKdV equations. The wave, group, and phase velocities of these envelope fractional 1-soliton solutions are related to the power laws of their amplitudes. These obtained fractional N-soliton solutions may be useful to explain the related super-dispersion transports of nonlinear waves in fractional nonlinear media.
