Adomian Decomposition Method for the One-dimensional Nonlocal Fisher-Kolmogorov-Petrovsky-Piskunov Equation

The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher-Kolmogorov-Petrovsky-Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.