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Some discussions about variable separation of nonlinear models using Riccati equation expansion method

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Abstract

Based on the Riccati equation expansion method with radical sign combined ansatz, nine kinds of variable separation solutions with different forms of (3+1)-dimensional Burgers equation are constructed. From these different solutions constructed by the Riccati equation expansion method, we confirm that these seem independent solutions exist some relations and actually depend on each other. Moreover, we discuss the construction of localized excitation based on variable separation solutions. Results indicate that for the (3+1)-dimensional two- or multi-component system, when we construct localized coherent structures for a special component based on variable separation solutions, we must note the corresponding structures constructed by the other component for the same equation for some nonlinear models in order to avoid the appearance of some divergent and un-physical structures. We hope that these results have potential application for the deep study of exact solutions of nonlinear models in physical, engineering and biophysical areas.

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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 No. 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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Authors and Affiliations

  1. School of Sciences, Zhejiang Agriculture and Forestry University, Lin’an, 311300, Zhejiang, People’s Republic of China

    Liang-Qian Kong & Chao-Qing Dai

  2. Zhejiang Provincial Key Laboratory of Chemical Utilization of Forestry Biomass, Zhejiang A & F University, Lin’an, 311300, Zhejiang, People’s Republic of China

    Chao-Qing Dai

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  1. Liang-Qian Kong
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Correspondence to Chao-Qing Dai.

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Kong, LQ., Dai, CQ. Some discussions about variable separation of nonlinear models using Riccati equation expansion method. Nonlinear Dyn 81, 1553–1561 (2015). https://doi.org/10.1007/s11071-015-2089-y

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  • DOI: https://doi.org/10.1007/s11071-015-2089-y

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