An exact soliton-like solution of cubic-quintic nonlinear Schro spacing diaeresis dinger equation with pure fourth order dispersion

We find analytically an exact soliton-like solution of cubic-quintic nonlinear Schrodinger equation (CQNLSE) with pure normal fourth-order dispersion (FOD). This exact solitary solution is fixed-parameter solitary wave, whose waveform is well described by hyperbolic secant function without oscillating tails. Those characteristics contribute importantly new information on solitons generation compared to the conventional pure-quartic soliton (PQS) in the absence of quintic nonlinearity. The numerical results verify that this exact solitary solution can preserve its shape. The formation of such solitary wave is a result of counterbalance between normal FOD as well as positive Kerr nonlinearity and negative quintic nonlinearity. The stability of such exact solitary wave is discussed as well. Although such exact solitary wave is linearly unstable in the presence of perturbation, our results disclose the role of quintic nonlinearity in the formation of high-energy PQS and its propagation, and also provide a way to control the generation of high-energy PQS laser pulse.

Automated summary

By analytically finding an exact solitary solution of the cubic-quintic nonlinear Schrodinger equation with pure normal fourth-order dispersion, we have shown that this solution can preserve its shape and is formed by a balance between different nonlinear effects. The role of quintic nonlinearity in generating high-energy pulses and the potential control over high-energy pulses have also been discussed in this study.