An exact soliton-like solution of cubic-quintic nonlinear Schrödinger equation with pure fourth order dispersion

Abstract

We find analytically an exact soliton-like solution of cubic-quintic nonlinear Schrödinger 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.

Keywords

• Fourth-order dispersion
• Cubic-quintic nonlinear Schrödinger equation
• Exact soliton-like solution
• Pure quartic soliton
• Soliton stability