$N$-soliton solutions of the Fokas-Lenells equation for the plasma ion-cyclotron waves: Inverse scattering transform approach

Abstract

We present a simple and constructive method to find $N$-soliton solutions of the equation suggested by Davydova and Lashkin to describe the dynamics of nonlinear ion-cyclotron waves in a plasma and subsequently known (in a more general form and as applied to nonlinear optics) as the Fokas-Lenells equation. Using the classical inverse scattering transform approach, we find bright $N$-soliton solutions, rational $N$-soliton solutions, and $N$-soliton solutions in the form of a mixture of exponential and rational functions. Explicit breather solutions are presented as examples. Unlike purely algebraic constructions of the Hirota or Darboux type, we also give a general expression for arbitrary initial data decaying at infinity, which contains the contribution of the continuous spectrum (radiation).

arXiv admin note: text overlap with arXiv:2103.10090

References in corpus (3)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• Perturbation theory for solitons of the Fokas--Lenells equation : Inverse scattering transform approach
• Blow-up solitons at the nonlinear stage of the two-stream instability in quantum plasmas