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Exact solutions of nonlocal Fokas-Lenells equation. (English) Zbl 1428.35545

Summary: In this paper we propose a nonlocal Fokas-Lenells (FL) equation which can be derived from the Kaup-Newell (KN) linear scattering problem. By constructing the Darboux transformation of nonlocal FL equation, we obtain its different kinds of exact solutions including bright/dark solitons, kink solutions, periodic solutions and several types of mixed soliton solutions. It is shown that the solutions of nonlocal FL equation possess different properties from the normal FL equation.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35B09 Positive solutions to PDEs
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