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arXiv · 1705.06836

Smooth positon solutions of the focusing modified Korteweg-de Vries equation

Qiuxia Xing·Zhiwei Wu·Dumitru Mihalache·Jingsong He
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Abstract

The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues $λ_{j}$ and the corresponding eigenfunctions of the associated Lax equation. The nonsingular $n$-positon solutions of the focusing mKdV equation are obtained in the special limit $λ_{j}\rightarrowλ_{1}$, from the corresponding $n$-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the $n$-positon solution into $n$ single-soliton solutions, the trajectories, and the corresponding "phase shifts" of the multi-positons are also investigated.

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Qiuxia Xing, Zhiwei Wu, Dumitru Mihalache, Jingsong He. 2017-05-19. Smooth positon solutions of the focusing modified Korteweg-de Vries equation. https://arxiv.org/abs/1705.06836

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