Abundance of stable stationary localized solutions to the generalized 1D Swift-Hohenberg equation
The authors consider the generalized Swift-Hohenberg equation \(u_t=\alpha u+\beta u^2 - u^3 - (1+\Delta)^2u\) and find a number of stationary localized solutions by using the theory of homoclinic orbits to a saddle-focus equilibrium and some results of symmetric differential operators along with computer simulations.
scientific article; zbMATH DE number 1107124
scientific article