Parkes, E.J. (2010) Observations on the tanhcoth expansion method for finding solutions to nonlinear evolution equations. Applied Mathematics and Computation, 217. pp. 17491754. ISSN 00963003

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

ID code:  27532 
Keywords:  nonlinear evolution equations, tanhfunction expansion method, tanhcoth function expansion method, solitary travelling waves., Mathematics, Computational Mathematics, Applied Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  28 Sep 2010 14:09 
Last modified:  15 Apr 2015 10:19 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/27532 
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