Inverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions
Yi Zhao, Engui Fan
Abstract
In this article, we focus on the inverse scattering transformation for the Fokas-Lenells (FL) equation with nonzero boundary conditions via the Riemann-Hilbert (RH) approach.Based on the Lax pair of the FL equation, the analyticity, symmetry and asymptotic behavior of the Jost solutions and scattering matrix are discussed in detail.With these results, we further present a generalized RH problem, from which a reconstruction formula between the solution of the FL equation and the Riemann-Hilbert problem is obtained.The N-soliton solutions of the FL equation is obtained by solving the RH problem.
Topics & Concepts
MathematicsTransformation (genetics)Inverse scattering problemMathematical analysisInverseBoundary (topology)Inverse scattering transformQuantum inverse scattering methodBoundary value problemScatteringInverse problemGeometryPhysicsBiochemistryOpticsChemistryGeneNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsFractional Differential Equations Solutions