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arXiv · 1607.05790

A self-adaptive moving mesh method for the short pulse equation via its hodograph link to the sine-Gordon equation

S. Sato·K. Oguma·T. Matsuo·B. -F. Feng
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Abstract

The short pulse equation was introduced by Schaefer--Wayne (2004) for modeling the propagation of ultrashort optical pulses. While it can describe a wide range of solutions, its ultrashort pulse solutions with a few cycles, which the conventional nonlinear Schroedinger equation does not possess, have drawn much attention. In such a region, existing numerical methods turn out to require very fine numerical mesh, and accordingly are computationally expensive. In this paper, we establish a new efficient numerical method by combining the idea of the hodograph transformation and the structure-preserving numerical methods. The resulting scheme is a self-adaptive moving mesh scheme that can successfully capture not only the ultrashort pulses but also exotic solutions such as loop soliton solutions.

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S. Sato, K. Oguma, T. Matsuo, B. -F. Feng. 2016-07-20. A self-adaptive moving mesh method for the short pulse equation via its hodograph link to the sine-Gordon equation. https://arxiv.org/abs/1607.05790

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