A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions

Abstract

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.

To appear in J. Phys. A: Math. Theor. 45(2012) May

References in corpus (4)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• Lattice representation and dark solitons of the Fokas-Lenells equation
• Two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions
• The bright $N$-soliton solution of a multi-component modified nonlinear Schrödinger equation

Cited by in corpus (4)

• The Fokas-Lenells equations: Bilinear approach
• Perturbation theory for solitons of the Fokas--Lenells equation : Inverse scattering transform approach
• Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces
• Linear interference and systematic soliton shape modulation by engineering plane wave background and soliton parameters