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Volume 10, Issue 4
Symbolic Computation of Lump Solutions to a Combined Equation Involving Three Types of Nonlinear Terms

Wen-Xiu Ma, Yi Zhang & Yaning Tang

DOI: 10.4208/eajam.151019.110420

East Asian J. Appl. Math., 10 (2020), pp. 732-745.

Published online: 2020-08

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  • Abstract

This paper aims to compute lump solutions to a combined fourth-order equation involving three types of nonlinear terms in (2+1)-dimensions via symbolic computations. The combined nonlinear equation contains all second-order linear terms and it possesses a Hirota bilinear form under two logarithmic transformations. Two classes of explicit lump solutions are determined, which are associated with two cases of the coefficients in the model equation. Two illustrative examples of the combined nonlinear equation are presented, along with lump solutions and their representative three-dimensional plots, contour plots and density plots.

  • Keywords

Soliton equation, lump solution, Hirota derivative, symbolic computation, dispersion relation.

  • AMS Subject Headings

35Q51, 35Q53, 37K40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-732, author = {Ma , Wen-XiuZhang , Yi and Tang , Yaning}, title = {Symbolic Computation of Lump Solutions to a Combined Equation Involving Three Types of Nonlinear Terms}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {732--745}, abstract = {

This paper aims to compute lump solutions to a combined fourth-order equation involving three types of nonlinear terms in (2+1)-dimensions via symbolic computations. The combined nonlinear equation contains all second-order linear terms and it possesses a Hirota bilinear form under two logarithmic transformations. Two classes of explicit lump solutions are determined, which are associated with two cases of the coefficients in the model equation. Two illustrative examples of the combined nonlinear equation are presented, along with lump solutions and their representative three-dimensional plots, contour plots and density plots.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.151019.110420 }, url = {http://global-sci.org/intro/article_detail/eajam/17953.html} }
TY - JOUR T1 - Symbolic Computation of Lump Solutions to a Combined Equation Involving Three Types of Nonlinear Terms AU - Ma , Wen-Xiu AU - Zhang , Yi AU - Tang , Yaning JO - East Asian Journal on Applied Mathematics VL - 4 SP - 732 EP - 745 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.151019.110420 UR - https://global-sci.org/intro/article_detail/eajam/17953.html KW - Soliton equation, lump solution, Hirota derivative, symbolic computation, dispersion relation. AB -

This paper aims to compute lump solutions to a combined fourth-order equation involving three types of nonlinear terms in (2+1)-dimensions via symbolic computations. The combined nonlinear equation contains all second-order linear terms and it possesses a Hirota bilinear form under two logarithmic transformations. Two classes of explicit lump solutions are determined, which are associated with two cases of the coefficients in the model equation. Two illustrative examples of the combined nonlinear equation are presented, along with lump solutions and their representative three-dimensional plots, contour plots and density plots.

Ma , Wen-XiuZhang , Yi and Tang , Yaning. (2020). Symbolic Computation of Lump Solutions to a Combined Equation Involving Three Types of Nonlinear Terms. East Asian Journal on Applied Mathematics. 10 (4). 732-745. doi:10.4208/eajam.151019.110420
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