<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e24" altimg="si8.svg"><mml:mi>N</mml:mi></mml:math>-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 Lashkin describe dynamics nonlinear ion-cyclotron waves in plasma subsequently known (in more general form as applied optics) Fokas-Lenells equation. Using classical inverse scattering transform approach, we bright solutions, rational mixture exponential functions. Explicit breather are presented examples. Unlike purely algebraic constructions Hirota or Darboux type, also give expression for arbitrary initial data decaying at infinity, which contains contribution continuous spectrum (radiation).