Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation

Wei Liu; Zhenyun Qin

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arXiv · 1711.06059

Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation

Wei Liu·Zhenyun Qin

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Abstract

Inspired by the works of Ablowitz, Mussliman and Fokas, a partial reverse space-time nonlocal Mel'nikov equation is introduced. This equation provides two dimensional analogues of the nonlocal Schrodinger-Boussinesq equation. By employing the Hirota's bilinear method, soliton, breathers and mixed solutions consisting of breathers and periodic line waves are obtained. Further, taking a long wave limit of these obtained soliton solutions, rational and semi-rational solutions of the nonlocal Mel'nikov equation are derived. The rational solutions are lumps. The semi-rational solutions are mixed solutions consisting of lumps, breathers and periodic line waves. Under proper parameter constraints, fundamental rogue waves and a semi-rational solutions of the nonlocal Schrodinger-Boussinesq equation are generated from solutions of the nonlocal Mel'nikov equation.

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BibTeX RIS

Wei Liu, Zhenyun Qin. 2017-11-16. Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation. https://arxiv.org/abs/1711.06059

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