A Fokas approach to the coupled modified nonlinear Schrodinger equation on the half-line

作者：Hu, Beibei; Xia, Tiecheng^*

来源：Mathematical Methods in the Applied Sciences, 2018, 41(13): 5112-5123.

DOI：10.1002/mma.5057

• Coupled modified nonlinear Schrodinger equation
• Fokas method
• initial-boundary value problem
• Riemann-Hilbert problem

In this work, we discuss the coupled modified nonlinear Schrodinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial-boundary value problem for the CMNLS equation related to a 3x3 matrix Lax pair on the half-line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3x3 matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter . Moreover, we also get that some spectral functions s() and S() are not independent of each other but meet a global relationship.

• 出版日期2018-9-15
• 单位上海大学; 滁州学院