A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation. I: Bright soliton solutions. (English) Zbl 1245.82055
Summary: We develop a direct method of solution for finding the bright \(N\)-soliton solution of the Fokas-Lenells derivative nonlinear Schrödinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.
MSC:
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35C08 | Soliton solutions |
82B26 | Phase transitions (general) in equilibrium statistical mechanics |