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arXiv · 1910.08921

The Riemann-Hilbert approach to focusing Kundu-Eckhaus equation with nonzero boundary conditions

Lili Wen·Engui Fan
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Abstract

In this article, we focus on investigating the focusing Kundu-Eckhaus equation with nonzero boundary condition. A appropriate two-sheeted Riemann surface is introduced to map the spectral parameter $k$ into a single-valued parameter $z$. Starting from the Lax pair of Kundu-Eckhaus equation,two kind of Jost solutions are construed. Further their asymptotic, analyticity, symmetries as well as spectral matrix are detailed analyzed. It is shown that the solution of Kundu-Eckhaus equation with nonzero boundary condition can characterized with a matrix Riemann-Hilbert problem. Then a formula of $N$-soliton solutions is derived by solving Riemann-Hilbert problem. As applications, the first-order explicit soliton solution is obtained.

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Lili Wen, Engui Fan. 2019-10-20. The Riemann-Hilbert approach to focusing Kundu-Eckhaus equation with nonzero boundary conditions. https://doi.org/10.1142/s0217984920503327

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