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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