Multi-bright-dark soliton solutions to the AB system in nonlinear optics |
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Authors: | Yunyun Zhai Lifei Wei Xianguo Geng Jiao Wei |
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Institution: | School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, China |
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Abstract: | The AB system is the basic integrable model to describe unstable baroclinic wave packets in geophysical fluids and the propagation of mesoscale gravity flows in nonlinear optics. On the basis of the spectral analysis of a Lax pair and the inverse scattering method, we establish the Riemann–Hilbert problem of the AB system. Then, the inverse problems are formulated and solved with the aid of the Riemann–Hilbert problem, from which the potentials can be reconstructed according to the asymptotic expansion of the sectional analytic function and the related symmetry relations. As an application, we obtain the multi-bright-dark soliton solutions to the AB system in the reflectionless case and discuss the dynamic behavior of elastic soliton collisions by choosing appropriate free parameters. |
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Keywords: | AB system multi-soliton structures Riemann–Hilbert problem |
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