Exact Solutions > Interesting Papers > N.A. Kudryashov. Seven common errors in finding exact solutions of nonlinear differential equations > 8. Seventh error... Seven common errors in finding exact solutions of nonlinear differential equations

 (8.1) 
Using
 (8.2) 
we obtain the linear equation of the second order
 (8.3) 
The solution of equation (8.1) takes the form
 (8.4) 
At first glance we obtain more general solution (8.4) of the Riccati equation then (5.7), but in fact these solutions are the same. We can see, that one of the constants can be removed by dividing the nominator and the denominator in solution (8.4) on C_{3} (or on C_{4}). Denoting (or ) we obtain the solution with the only arbitrary constant.
Example 7b. Solution of the Sharma  Tasso  Olver equation.
In example 2f we have obtained the solution of Eq.(3.36) in the form
 (8.5) 
However Eq.(3.36) has the second order, but solution (8.5) contains tree arbitrary constants. Sometimes it is convenient to leave three constants in solution (8.5), but we have to remember that solution (8.5) is not the general solution and one of these constants is extra. We can remove one of the constants as in example 7a and can write the general solution of Eq.(3.36) in the form
 (8.6) 
Solution (8.6) of Eq.(3.36) is not worse then solution (8.5), but this solution is the general solution by definition and all other solution can be found from this one.
Example 7c. Solution (6.5) of the modified Benjamin  Bona  Mahony equation (6.3) [63]
 (8.7) 
Solution (8.7) has three arbitrary constants a_{0}, b_{0} and b_{1}, but in fact this solution can be simplified to the form with one arbitrary constant as it was demonstrated in example 5c.
Example 7d. ”New exact solution” of the Riccati equation by Dai and Wang [76]
 (8.8) 
Dai and Wang [76] had been looking for the ”new exact solutions” of the Riccati equation (8.8) and obtained five solutions. One of them (solution (17) [76]) takes the form
 (8.9) 
We can see, that solution (8.9) has three arbitrary constants, but two of them certainly can be removed.
Example 7e. Solutions of the Burgers  Huxley equation by Chun [68].
Using the Exp  function method Chun [68] obtained the generalized solitary wave solutions of the Burgers — Huxley equation (see, Eq.(8.10) in example 6e). One of his solution (solution (32) in [68]) takes the form
 (8.10) 
The Burgers — Huxley equation is the second order one but solution (8.10) has three arbitrary constants. We suggested that this solution is incorrect. We checked this solution and have convinced that this solution does not satisfy Eq.(7.19).
Especially many solutions of equations with superfluous constants were obtained by means of the Exp  function method. Such examples can be found in many papers.
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