Xinyue Li, Zhixin Zhang, Qiulan Zhao , Chuanzhong Li
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引用次数: 2
Abstract
The short pulse equation is able to describe ultra short pulse, which plays a crucial part in the field of optical fiber propagation. In this paper, we investigate a generalized complex short pulse equation and its two-component generalization. We first prove that they are Lax integrable. Subsequently, we obtain their new Lax pairs through hodograph transformation to carry out Darboux transformation, respectively. For the generalized complex short pulse equation, we provide a different Darboux matrix and verify that it is feasible, then we focus on higher-order semi-rational soliton solutions by means of generalized Darboux transformation. For the coupled generalized complex short pulse equations, we apply Darboux transformation to discuss exact solutions by choosing different seed solutions.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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