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Re-study on localized structures based on variable separation solutions from the modified tanh-function method

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Abstract

We derive variable separation solutions of the (\(1+1\))-dimensional KdV-type model by means of the modified tanh-function method with three different ansätz. Superficially speaking, the positive and negative power-symmetric ansatz seems to be better than the positive-power ansatz and radical sign combined ansatz because the positive and negative power-symmetric ansatz can construct the most forms of variable separation solutions. Actually, we find that various “different” solutions obtained by the modified tanh-function method are not independent, and many of the so-called new solutions are equivalent to one another. Moreover, in the two- or multi-component system, if we construct localized coherent structures for a special component based on variable separation solutions, we must note the structure constructed by the other component for the same equation in order to avoid the appearance of some divergent and un-physical structures. We hope that these results above contribute to the analysis on exact solutions and the construction of localized structures for other nonlinear models.

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Acknowledgments

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13F050006), the National Natural Science Foundation of China (Grant Nos. 11404289 and 11375007), and the Scientific Research and Developed Fund of Zhejiang A & F University (Grant No. 2014FR020). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China and Youth Top-notch Talent Development and Training Program of Zhejiang A&F University.

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  1. School of Sciences, Zhejiang A & F University, Lin’an, Zhejiang, 311300, People’s Republic of China

    Yue-Yue Wang, Yu-Peng Zhang & Chao-Qing Dai

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  1. Yue-Yue Wang
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Correspondence to Yue-Yue Wang.

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Wang, YY., Zhang, YP. & Dai, CQ. Re-study on localized structures based on variable separation solutions from the modified tanh-function method. Nonlinear Dyn 83, 1331–1339 (2016). https://doi.org/10.1007/s11071-015-2406-5

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  • DOI: https://doi.org/10.1007/s11071-015-2406-5

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