Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
arXiv:2309.02129 · doi:10.1088/1402-4896/ad302c
Abstract
We construct quasiparticles-like solutions to the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) with a nonlocal nonlinearity using the method of semiclassically concentrated states in the weak diffusion approximation. Such solutions are of use for predicting the dynamics of population patterns. The interaction of quasiparticles stems from nonlocal competitive losses in the FKPP model. We developed the formalism of our approach relying on ideas of the Maslov method. The construction of the asymptotic expansion of a solution to the original nonlinear evolution equation is based on solutions to an auxiliary dynamical system of ODEs. The asymptotic solutions for various specific cases corresponding to various spatial profiles of the reproduction rate and nonlocal competitive losses are studied within the framework of the approach proposed.
27 pages, 2 figures
References in corpus (5)
- Lecture notes on Generalised Hydrodynamics
- From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation
- Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity
- Semiclassical approach to the nonlocal nonlinear Schrödinger equation with a non-Hermitian term
- Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity