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Lump solutions to dimensionally reduced \(\varvec{p}\)-gKP and \(\varvec{p}\)-gBKP equations


Based on generalized bilinear forms, lump solutions, rationally localized in all directions in the space, to dimensionally reduced p-gKP and p-gBKP equations in (2+1)-dimensions are computed through symbolic computation with Maple. The sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions are presented. The resulting lump solutions contain six parameters, two of which are totally free, due to the translation invariance, and the other four of which only need to satisfy the presented sufficient and necessary conditions. Their three-dimensional plots with particular choices of the involved parameters are made to show energy distribution.

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The work was supported in part by NNSFC under the Grants 11371326 and 11271008, the distinguished professorship of the Shanghai University of Electric Power, the Fundamental Research Funds for the Central Universities (2013XK03), the Natural Science Foundation of Shandong Province (Grant No. ZR2013AL016), Zhejiang Innovation Project of China (Grant No. T200905), the First-class Discipline of Universities in Shanghai and the Shanghai Univ. Leading Academic Discipline Project (No. A.13-0101-12-004). ZY was supported by the NNSFC under the Grant 11571079, Shanghai Pujiang Program (No. 14PJD007) and the Natural Science Foundation of Shanghai (No. 14ZR1403500 ), and the Young Teachers Foundation (No. 1411018) of Fudan university. XL was supported by NNSFC under the Grant 61308018 and the Fundamental Research Funds for the Central Universities (2014RC019 and 2015JBM111).

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Ma, W.X., Qin, Z. & Lü, X. Lump solutions to dimensionally reduced \(\varvec{p}\)-gKP and \(\varvec{p}\)-gBKP equations. Nonlinear Dyn 84, 923–931 (2016).

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