Applying new wavelet transform method on the generalized-FKPP equation

The numerous methods for solving differential equations exist, every method have benefits and drawbacks, in this field, the combined methods are very useful, one of them is the wavelet transform method (WTM). This method based on the wavelets and corresponding wavelet transform, that dependent on the differential invariants obtained by the Lie symmetry method. In this paper, we apply the WTM on the generalized version of FKPP equation (GFKPP) with non-constant coefficient  futt(x,t)+ut(x,t)=uxx(x,t)+u(x,t)-u۲(x,t) where f is a smooth function of either x or t. We will see for suitable wavelets, this method proposes the interesting solutions.

Keywords:

Wavelet , Quasi-wavelet , Mother wavelet , The wavelet transform , Differential invariants , The GFKPP equation