Exact Solutions > Interesting Papers > N.A. Kudryashov. Seven common errors in finding exact solutions of nonlinear differential equations > 4. Third error... Seven common errors in finding exact solutions of nonlinear differential equations

 (4.1) 
to solve this equation by so called ”the modified extended tanh  function method”.
It is well known, that by using the ColeHopf transformation [52, 53]
 (4.2) 
we can write the equality
 (4.3) 
From the last relation we can see, that each solution of the heat equation
 (4.4) 
gives the solution of the Burgers equation by formula (4.2).
However to find the solutions of the Burgers equation Soliman [51] used the travelling wave solutions , and from Eq.(4.1) after integration with respect to the author obtained the equation in the form
 (4.5) 
The constant of integration he took to be equal to zero. The general solution of Eq.(4.5) takes the form
 (4.6) 
where C_{2} is an arbitrary constant.
The general solution of Eq.(4.5) has the only arbitrary constant. But if we take nonzero constant of integration in Eq.(4.5), we can have two arbitrary constants in the solution.
Example 3b. Reduction of the (2+1)  dimensional Konopelchenko  Dubrovsky equation by Abdou [54]
(4.7) 
(4.8) 
(4.9) 
However multiplying Eq.(4.9) on and integrating this equation with respect to again, we have the equation
(4.10) 
Example 3c. Reduction of the Ito equation by Wazwaz [55]
(4.11) 
The author [55] looked for the solutions of Eq. (4.11) taking into account the travelling wave
(4.12) 
Substituting (4.12) into (4.11) Wazwaz obtained when and the equation in the form
(4.13) 
Integrating Eq.(4.13) twice with respect to one can have the equation
(4.14) 
(4.15) 
The general solution of this equation was discussed above in example 2b.
However the author [55] looked for solutions of Eq. (4.14) for C_{8} = 0 and C_{9} = 0 taking into consideration the tanh  coth method and did not present the general solution of Eq. (4.13).
Example 3d. Reduction of the Boussinesq equation by Bekir [32]
(4.16) 
(4.17) 
In fact, from Eq.(4.16) we obtain the second order differential equation in the form
(4.18) 
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