N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Author to whom correspondence should be addressed.
Received: 6 June 2019 / Revised: 17 June 2019 / Accepted: 20 June 2019 / Published: 22 June 2019
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In this paper, a kind of nonlinear Schrödinger (NLS) equation, called an NLS-like equation, is Riemann–Hilbert investigated. We construct a
Lax pair associated with the NLS equation and combine the spectral analysis to formulate the Riemann–Hilbert (R–H) problem. Then, we mainly use the symmetry relationship of potential matrix Q
to analyze the zeros of
; the N-soliton solutions of the NLS-like equation are expressed explicitly by a particular R–H problem with an unit jump matrix. In addition, the single-soliton solution and collisions of two solitons are analyzed, and the dynamic behaviors of the single-soliton solution and two-soliton solutions are shown graphically. Furthermore, on the basis of the R–H problem, the evolution equation of the R–H data with the perturbation is derived.
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MDPI and ACS Style
Lin, Y.; Dong, H.; Fang, Y. N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem. Symmetry 2019, 11, 826.
Lin Y, Dong H, Fang Y. N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem. Symmetry. 2019; 11(6):826.
Lin, Yuxin; Dong, Huanhe; Fang, Yong. 2019. "N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem." Symmetry 11, no. 6: 826.
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