Abstract
With symbolic computation, two classes of lump solutions to the dimensionally reduced equations in (2+1)-dimensions are derived, respectively, by searching for positive quadratic function solutions to the associated bilinear equations. To guarantee analyticity and rational localization of the lumps, two sets of sufficient and necessary conditions are presented on the parameters involved in the solutions. Localized characteristics and energy distribution of the lump solutions are also analyzed and illustrated.
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Acknowledgments
This work is supported by the 111 Project of China (B16002), the National Natural Science Foundation of China under Grant No. 61308018, by China Postdoctoral Science Foundation under Grant No. 2014T70031, by the Fundamental Research Funds for the Central Universities of China (2015JBM111). The second author is supported in part by the National Natural Science Foundation of China under Grant Nos. 11371326 and 11271008, Natural Science Foundation of Shanghai under Grant No. 11ZR1414100, Zhejiang Innovation Project of China under Grant No. T200905, the First-class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project (No. A13-0101-12-004) and the Distinguished Professorship at Shanghai University of Electric Power.
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Lü, X., Ma, WX. Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dyn 85, 1217–1222 (2016). https://doi.org/10.1007/s11071-016-2755-8
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DOI: https://doi.org/10.1007/s11071-016-2755-8