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CONCLUSION

This study has given us a lot of  informations about this equation and the means to approach it numerically:
Indeed, we have studied its equilibriums and ploted its trajectories for specific limits conditions and differents values of the parameters. Futhermore, we have established a criterion of numerical stability for the numerical scheme we have taken.

Nevertheless, a lot of problems remain like the stability. Indeed, the study of the stabilty of this equation isn't simple. Indeed a little study of stabilty seems to show that stability depends on the parameters, but on the limits conditions and L too.

Perhaps, we could see the instabilities of this equation like the instabilities of the non linear term of the equation modified by the couple K.
 
 

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