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arXiv · 2001.03865

Riemann-Hilbert approach and $N$-soliton solutions for a new four-component nonlinear Schr\"odinger equation

Xin-Mei Zhou·Shou-Fu Tian·Jin-Jie Yang·Jin-Jin Mao
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Abstract

A new four-component nonlinear Schr\"{o}dinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a $5\times5$ matrix spectral problem for the four-component nonlinear Schr\"{o}dinger equation. Then based on the Lax pair, we analyze the spectral problem and the analytical properties of the Jost functions, from which the Riemann-Hilbert problem of the equation is successfully established. Moreover, we obtain the $N$-soliton solutions of the equation by solving the Riemann-Hilbert problem without reflection. Finally, we derive two special cases of the solutions to the equation for $N=1$ and $N=2$, and the local structure and dynamic behavior of the one-and two-soliton solutions are analyzed graphically.

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Xin-Mei Zhou, Shou-Fu Tian, Jin-Jie Yang, Jin-Jin Mao. 2020-01-12. Riemann-Hilbert approach and $N$-soliton solutions for a new four-component nonlinear Schr\"odinger equation. https://arxiv.org/abs/2001.03865

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