Name
Abstract | ||
|---|---|---|
The solution of the initial value problem (IVP) for the Fokas–Lenells equation (FLE) was constructed in terms of the solution M(x,t,k) of a 2 × 2 matrix Riemann–Hilbert problem (RHP) as k→∞, and the one-soliton solution of the FLE was derived based on this Riemann–Hilbert problem, in Lenells and Fokas (2009). However, in fact, the derivative with respect to x of the solution of the FLE (ux(x,t)) was recovered from the RHP as k→∞. In this paper, we construct the solution of the FLE in terms of the RHP as k→0, because the Lax pair of the FLE contains the negative order of the spectral variable k. We show that the one-soliton solution of the FLE obtained in this paper is the same as Lenells and Fokas (2009), but avoiding a complex integral. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.aml.2018.07.027 | Applied Mathematics Letters |
Keywords | Field | DocType |
Riemann–Hilbert problem,Fokas–Lenells equation,Initial value problem,Negative order Lax pair | Mathematical analysis,Matrix (mathematics),Riemann–Hilbert problem,Pure mathematics,Lax pair,Initial value problem,Mathematics | Journal |
Volume | ISSN | Citations |
87 | 0893-9659 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |