Existence of Peregrine type solutions in fractional reaction–diffusion equations - Agustin Besteiro; Diego Rial (Electronic Journal of Qualitative Theory of Differential Equations, 2019)
In this article, we analyze the existence of Peregrine type solutions for the fractional reaction–diffusion equation by applying splitting-type methods. Peregrine type functions have two main characteristics, these are direct sum of functions of periodic type and functions that tend to zero at infinity. Well-posedness results are obtained for each particular characteristic, and for both combined.