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Volume 25, Issue 4
Some Exact Solutions of Two Fifth Order KdV-type Nonlinear Partial Differential Equations

Abdus Sattar Mia & Tania Akter

DOI: 10.4208/jpde.v25.n4.4

J. Part. Diff. Eq., 25 (2012), pp. 356-365.

Published online: 2012-12

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  • Abstract

We consider the generalized integrable fifth order nonlinear Korteweg-de Vries (fKdV) equation. The extended Tanh method has been used rigorously, by computational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact solutions are found for the two fifth order KdV-type equations given by the Caudrey-Dodd-Gibbon equation and the another fifth order equation. The obtained solutions include solitary wave solution for both the two equations.

  • Keywords

5th order KdV-type equation extended Tanhmethod CDG equation exact solutions solitary wave solution

  • AMS Subject Headings

35C05, 35C07, 35C08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

sattar_ju@yahoo.com (Abdus Sattar Mia)

taniawub@gmail.com (Tania Akter)

  • BibTex
  • RIS
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@Article{JPDE-25-356, author = {Mia , Abdus Sattar and Akter , Tania}, title = {Some Exact Solutions of Two Fifth Order KdV-type Nonlinear Partial Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {4}, pages = {356--365}, abstract = {

We consider the generalized integrable fifth order nonlinear Korteweg-de Vries (fKdV) equation. The extended Tanh method has been used rigorously, by computational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact solutions are found for the two fifth order KdV-type equations given by the Caudrey-Dodd-Gibbon equation and the another fifth order equation. The obtained solutions include solitary wave solution for both the two equations.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/5191.html} }
TY - JOUR T1 - Some Exact Solutions of Two Fifth Order KdV-type Nonlinear Partial Differential Equations AU - Mia , Abdus Sattar AU - Akter , Tania JO - Journal of Partial Differential Equations VL - 4 SP - 356 EP - 365 PY - 2012 DA - 2012/12 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/5191.html KW - 5th order KdV-type equation KW - extended Tanhmethod KW - CDG equation KW - exact solutions KW - solitary wave solution AB -

We consider the generalized integrable fifth order nonlinear Korteweg-de Vries (fKdV) equation. The extended Tanh method has been used rigorously, by computational program MAPLE, for solving this fifth order nonlinear partial differential equation. The general solutions of the fKdV equation are formed considering an ansatz of the solution in terms of tanh. Then, in particular, some exact solutions are found for the two fifth order KdV-type equations given by the Caudrey-Dodd-Gibbon equation and the another fifth order equation. The obtained solutions include solitary wave solution for both the two equations.

Abdus Sattar Mia & Tania Akter. (2019). Some Exact Solutions of Two Fifth Order KdV-type Nonlinear Partial Differential Equations. Journal of Partial Differential Equations. 25 (4). 356-365. doi:10.4208/jpde.v25.n4.4
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