Exact Solutions > Interesting Papers > N.A. Kudryashov. Seven common errors in finding exact solutions of nonlinear differential equations > 6. Fifth error... Seven common errors in finding exact solutions of nonlinear differential equations

 (6.1) 
It is seen, that the last expression is better for understanding, then the solution by Öziş and Aslan.
Example 5b. Solutions of the Konopelchenko  Dubrovsky equation (4.7) by Abdou [54].
By means of the Exp  function method Abdou [54] obtained some solitary wave solutions of Eq. (4.7), but some solutions can be simplified. For example solution (42) in [54] reduces to
 (6.2) 
Example 5c. Solution of the modified Benjamin  Bona  Mahony equation by Yusufoǧlu [63]
 (6.3) 
Using the travelling wave the author [63] obtained the equation
 (6.4) 
Yusufoǧlu [63] found the solution of Eq.(6.4) in the form
 (6.5) 
Solution (6.5) has three arbitrary constants a_{0}, b_{0} and b_{1}, but in fact this solution can be simplified using the set of equalities
 (6.6) 
We can see, that solution (6.6) contains the only arbitrary constant .
Note that Eq.(6.3) can be easy transformed to the modified KdV equation and this equation is not the BBM equation.
Example 5d. Solutions of the fifth  order KdV equation by Chun [64]
 (6.7) 
Using the Exp  function method, Chun obtained seventeen exact solutions of Eq. (6.7) [64]. His first solution (formula (25) in [64]) can be simplified to the trivial solution, because
 (6.8) 
The sixth solution by Chun (formula (30) [64]) can be simplified to the trivial solution as well
 (6.9) 
The thirteenth (as well as the fourteenth and the fifteenth) solution (formula (69) in paper [64]) is also constant as we can see from the equality
 (6.10) 
We recognized, that among seventeen solutions presented by Chun in his paper twelve solutions (25), (27), (28) (30), (49), (51) (53), (55), (57), (69), (70) and (71) satisfy the fifthorder KdV equation, but solutions (25), (30), (69), (70) and (71) are trivial ones (constants) and (51) is not the solitary wave solution. Six solutions (25), (27), (49), (53), (55) and (57) are solitary wave solutions, but these ones are known and can be found by means of other methods.
Example 5e. Solutions of the improved Boussinesq equation by Abdou and co authors [65].
Using the Exp  function method Abdou and his co  authors looked for the solitary wave solutions of the improved Bouusinesq equation
 (6.11) 
In the travelling wave Eq.(6.13) takes the form
 (6.12) 
The authors found several solutions of Eq.(6.12). One of them takes the form
 (6.13) 
However this solution can be presented as
 (6.14) 
Solution (6.14) can be obtained by many methods.
We have often observed the fifth error studying the application of the Exp  function method.
Other examples of the fifth error are given in our recent papers [42, 46].
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