### Abstract

Original language | English |
---|---|

Pages (from-to) | 1749-1754 |

Number of pages | 6 |

Journal | Applied Mathematics and Computation |

Volume | 217 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- nonlinear evolution equations
- tanh-function expansion method
- tanh-coth function expansion method
- solitary travelling waves.

### Cite this

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*Applied Mathematics and Computation*, vol. 217, pp. 1749-1754. https://doi.org/10.1016/j.amc.2009.11.037

**Observations on the tanh-coth expansion
method for finding solutions to nonlinear
evolution equations.** / Parkes, E.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations

AU - Parkes, E.J.

PY - 2010

Y1 - 2010

N2 - The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s. It usually delivers three types of solution, namely a tanh-function expansion, a coth-function expansion, and a tanh-coth expansion. It is known that, for every tanh-function expansion solution, there is a corresponding coth-function expansion solution. It is shown that there is a tanh-coth expansion solution that is merely a disguised version of the coth solution. In many papers, such tanh-coth solutions are erroneously claimed to be 'new'. However, other tanh-coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh-function method. Similar remarks apply to tan, cot and tan-cot expansion solutions.

AB - The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the 1990s. It usually delivers three types of solution, namely a tanh-function expansion, a coth-function expansion, and a tanh-coth expansion. It is known that, for every tanh-function expansion solution, there is a corresponding coth-function expansion solution. It is shown that there is a tanh-coth expansion solution that is merely a disguised version of the coth solution. In many papers, such tanh-coth solutions are erroneously claimed to be 'new'. However, other tanh-coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh-function method. Similar remarks apply to tan, cot and tan-cot expansion solutions.

KW - nonlinear evolution equations

KW - tanh-function expansion method

KW - tanh-coth function expansion method

KW - solitary travelling waves.

UR - http://www.scopus.com/inward/record.url?scp=77953131964&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2009.11.037

DO - 10.1016/j.amc.2009.11.037

M3 - Article

VL - 217

SP - 1749

EP - 1754

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -