Data-Driven Solutions for the Integer and Fractional Order Derivative Nonlinear Schr?dinger Equation via Fourier Neural Operator Approach
In this paper,we utilize the Fourier neural operator(FNO)for the first time to investigate the derivative nonlinear Schrödinger(DNLS)equation and frac-tional derivative nonlinear Schrödinger(fDNLS)equation.For the DNLS equation,we successfully establish the mappings between the initial conditions of the equation and their respective solutions.The transition process of the soliton to the M-type wave is studied,and the periodic solution is also obtained.Simultaneously,the FNO learning method is employed to investigate the transformation process of the period-ical rogue wave.Moreover,we focus on learning the mapping between the fractional order exponential space and the soliton in the fDNLS equation.By comparing the data-driven solution with the exact solution,the powerful approximation capability of the FNO network is highlighted.Finally,we discuss the effects of the full-connected layer P and the activation function on the characterization ability of the network.
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