Dbar-Dressing Method and N -Soliton Solutions of the Derivative NLS Equation with Non-Zero Boundary Conditions

Hui Zhou, Yehui Huang and Yuqin Yao ()
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Hui Zhou: College of Science, China Agricultural University, Beijing 100083, China
Yehui Huang: School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
Yuqin Yao: College of Science, China Agricultural University, Beijing 100083, China

Mathematics, 2022, vol. 10, issue 23, 1-14

Abstract: The Dbar-dressing method is extended to investigate the derivative non-linear Schrödinger equation with non-zero boundary conditions (DNLSENBC). Based on a meromorphic complex function outside an annulus with center 0, a local Dbar-problem inside the annulus is constructed. By use of the asymptotic expansion at infinity and zero, the spatial and temporal spectral problems of DNLSENBC are worked out. Thus, the relation between the potential of DNLSENBC with the solution of the Dbar-problem is established. Further, symmetry conditions and a special spectral distribution matrix are presented to construct the explicit solutions of DNLSENBC. In addition, the explicit expressions of the soliton solution, the breather solution and the solution of the interaction between solitons and breathers are given.

Keywords: Dbar-dressing method; Cauchy matrix; Lax pair; soliton solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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