Numerical continuation for fractional PDEs: sharp teeth and bloated snakes
نویسندگان
چکیده
Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical numerical approaches. The purpose of this work is study the effects spectral Laplacian on bifurcation structure reaction-diffusion systems bounded domains. In order do we use advanced continuation techniques compute solution branches. Since current available packages only support standard Laplacian, first extend pde2path software treat PDEs. new capabilities then applied Allen-Cahn equation, Swift-Hohenberg equation Schnakenberg system (in which each replaced by Laplacian). Our reveals some common effects, contributes a better understanding in generic systems. particular, investigate changes snaking diagrams also spatial non-trivial steady states upon variation Laplacian. results show that can induce very significant qualitative quantitative global structures.
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2021
ISSN: ['1878-7274', '1007-5704']
DOI: https://doi.org/10.1016/j.cnsns.2021.105762