Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations

Wei-Kang Xun; Shou-Fu Tian

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arXiv · 2005.03319

Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations

Wei-Kang Xun·Shou-Fu Tian

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Abstract

In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of this is to study the soliton solutions of the coupled Fokas-Lenells(FL) equations for any positive integer $N$, which have more complex linear relationship than the analogues reported before. We first analyze the spectral analysis of the Lax pair associated with a $(N+1)\times (N+1)$ matrix spectral problem for the $N$-component FL equations. Then, a kind of RH problem is successfully formulated. By introducing the special conditions of irregularity and reflectionless case, the $N$-soliton solution formula of the equations are derived through solving the corresponding RH problem. Furthermore, take $N=2,3$ and $4$ for examples, the localized structures and dynamic propagation behavior of their soliton solutions and their interactions are discussed by some graphical analysis.

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BibTeX RIS

Wei-Kang Xun, Shou-Fu Tian. 2020-05-07. Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations. https://arxiv.org/abs/2005.03319

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