The Fokas-Lenells equations: Bilinear approach

Abstract

In this paper, the Fokas-Lenells equations are investigated via bilinear approach. We bilinearize the unreduced Fokas-Lenells system, derive double Wronskian solutions, and then, by means of a reduction technique we obtain variety of solutions of the reduced equations. This enables us to have a full profile of solutions of the classical and nonlocal Fokas-Lenells equations. Some obtained solutions are illustrated based on asymptotic analysis. As a notable new result, we obtain solutions to the Fokas-Lenells equation, which are related to real discrete eigenvalues and not reported before in the analytic approaches. These solutions behave like (multi-)periodic waves or solitary waves with algebraic decay. In addition, we also obtain solutions to the two-dimensional massive Thirring model from those of the Fokas-Lenells equation.

arXiv comment32 pages, 11 figures, appendixes and references updated

References in corpus (17)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• Bilinearization of a Generalized Derivative Nonlinear Schrödinger equation
• Rogue waves of the Fokas-Lenells equation
• On a novel integrable generalization of the sine-Gordon equation
• General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation
• Darboux transformations and global explicit solutions for nonlocal Davey-Stewartson I equation
• A Novel Hierarchy of Integrable Lattices
• Lattice representation and dark solitons of the Fokas-Lenells equation
• A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions
• Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems
• Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation with step-like initial data
• Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
• Multi-place nonlocal systems
• Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data
• Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
• New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential
• Discrete Symmetries and Nonlocal Reductions

Cited by in corpus (3)

• Solutions to integrable space-time shifted nonlocal equations
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions