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

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).(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

We propose a straightforward and systematic approach to obtain N-soliton solutions for the equation that describes the dynamics of nonlinear ion-cyclotron waves in plasma, known as the Fokas-Lenells equation. By utilizing the classical inverse scattering transform method, we derive bright N-soliton solutions, rational N-soliton solutions, and N-soliton solutions in the form of exponential and rational functions. Additionally, we provide explicit examples of breather solutions and a general expression for arbitrary initial data decaying at infinity, accounting for the contribution of the continuous spectrum (radiation).