Volume 29, Issue 2
Solitary Wave Solutions to the ZKBBM Equation and the KPBBM Equation Via the Modified Simple Equation Method

J. Akter & M. Ali Akbar

J. Part. Diff. Eq., 29 (2016), pp. 143-160.

Published online: 2016-07

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  • Abstract

In this article, the modified simple equation method (MSE) is used to acquire exact solutions to nonlinear evolution equations (NLEEs) namely the Zakharov- Kuznetsov Benjamin-Bona-Mahony equation and the Kadomtsov-Petviashvilli Benjamin- Bona-Mahony equation which have widespread usage in modern science. The MSE method is ascending and useful mathematical tool for constructing exact traveling wave solutions to NLEEs in the field of science and engineering. By means of this method we attained some significant solutions with free parameters and for special values of these parameters, we found some soliton solutions derived from the exact solutions. The solutions obtained in this article have been shown graphically and also discussed physically.

  • Keywords

Modified simple equation method nonlinear evolution equations homogeneous balance soliton solutions Zakharov-Kuznetsov Benjamin-Bona-Mahony equation Kadomtsov-Petviashvilli Benjamin-Bona-Mahony equation

  • AMS Subject Headings

35C07 35C08 35K05 35P99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

j.akter7@gmail.com (J. Akter)

ali_math74@yahoo.com (M. Ali Akbar)

  • BibTex
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  • TXT
@Article{JPDE-29-143, author = {Akter , J. and Akbar , M. Ali }, title = {Solitary Wave Solutions to the ZKBBM Equation and the KPBBM Equation Via the Modified Simple Equation Method}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {2}, pages = {143--160}, abstract = { In this article, the modified simple equation method (MSE) is used to acquire exact solutions to nonlinear evolution equations (NLEEs) namely the Zakharov- Kuznetsov Benjamin-Bona-Mahony equation and the Kadomtsov-Petviashvilli Benjamin- Bona-Mahony equation which have widespread usage in modern science. The MSE method is ascending and useful mathematical tool for constructing exact traveling wave solutions to NLEEs in the field of science and engineering. By means of this method we attained some significant solutions with free parameters and for special values of these parameters, we found some soliton solutions derived from the exact solutions. The solutions obtained in this article have been shown graphically and also discussed physically.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n2.5}, url = {http://global-sci.org/intro/article_detail/jpde/5085.html} }
TY - JOUR T1 - Solitary Wave Solutions to the ZKBBM Equation and the KPBBM Equation Via the Modified Simple Equation Method AU - Akter , J. AU - Akbar , M. Ali JO - Journal of Partial Differential Equations VL - 2 SP - 143 EP - 160 PY - 2016 DA - 2016/07 SN - 29 DO - http://dor.org/10.4208/jpde.v29.n2.5 UR - https://global-sci.org/intro/jpde/5085.html KW - Modified simple equation method KW - nonlinear evolution equations KW - homogeneous balance KW - soliton solutions KW - Zakharov-Kuznetsov Benjamin-Bona-Mahony equation KW - Kadomtsov-Petviashvilli Benjamin-Bona-Mahony equation AB - In this article, the modified simple equation method (MSE) is used to acquire exact solutions to nonlinear evolution equations (NLEEs) namely the Zakharov- Kuznetsov Benjamin-Bona-Mahony equation and the Kadomtsov-Petviashvilli Benjamin- Bona-Mahony equation which have widespread usage in modern science. The MSE method is ascending and useful mathematical tool for constructing exact traveling wave solutions to NLEEs in the field of science and engineering. By means of this method we attained some significant solutions with free parameters and for special values of these parameters, we found some soliton solutions derived from the exact solutions. The solutions obtained in this article have been shown graphically and also discussed physically.
J. Akter & M. Ali Akbar. (2019). Solitary Wave Solutions to the ZKBBM Equation and the KPBBM Equation Via the Modified Simple Equation Method. Journal of Partial Differential Equations. 29 (2). 143-160. doi:10.4208/jpde.v29.n2.5
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