Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrödinger Equations on the Half-line

Bei-bei Hu 2 , 3 , Tie-cheng Xia 1 , Ning Zhang 4  and Jin-bo Wang 5
  • 1 Department of Mathematics, Shanghai University, 200444, Shanghai, China
  • 2 Department of Mathematics, Shanghai University, 200444, Shanghai, China
  • 3 School of Mathematics and Finance, Chuzhou University, 239000, Anhui, China
  • 4 Department of Basical Courses, Shandong University of Science and Technology, 271019, Taian, China
  • 5 Science and Technology on Communication Security Laboratory, 610041, Chengdu, China
Bei-bei Hu
  • Department of Mathematics, Shanghai University, Shanghai, 200444, China
  • School of Mathematics and Finance, Chuzhou University, Anhui, 239000, China
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, Tie-cheng Xia, Ning Zhang and Jin-bo Wang

Abstract

In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution {q1(x,t),q2(x,t)} exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter λ.

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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.

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