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arXiv · 1612.06723

Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence

Li-Yuan Ma·Shou-Feng Shen·Zuo-Nong Zhu
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Abstract

In this paper, we prove that the nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity, 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation(DT) for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton and periodic solutions are derived.

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Li-Yuan Ma, Shou-Feng Shen, Zuo-Nong Zhu. 2016-12-20. Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence. https://arxiv.org/abs/1612.06723

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