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The computation of coefficients of amplitude systems for Turing bifurcations is a straightforward but sometimes elaborate task, in particular for 2D or 3D wave vector lattices. The Matlab tool ampsys automates such computations for two classes of problems, namely scalar equations of Swift-Hohenberg type and generalizations, and reaction-diffusion systems with an arbitrary number of components. The tool is designed to require minimal user input, and for a number of cases can also deal with symbolic computations. After a brief review of the setup of amplitude systems we explain the tool by a number of 1D, 2D and 3D examples over various wave vector lattices.
We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review general co
We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. See [Uecker, Comm. in Comp. Phys., 2019] for a description
Stability of cylindrical and spherical crystals growing from a supersaturated solution (in Mullins-Sekerkas approximation) is considered using the maximum entropy production principle. The concept of the binodal of the nonequilibrium (morphological)
The localization characters of the first-order rogue wave (RW) solution $u$ of the Kundu-Eckhaus equation is studied in this paper. We discover a full process of the evolution for the contour line with height $c^2+d$ along the orthogonal direction
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger equation and syst