title: On small stationary localized solutions for the generalized 1-D Swift-Hohenberg equation.
abstract: We prove the existence of small localized stationary solutions for the generalized Swift-Hohenberg equation and find under some assumption a part of a boundary of their existence in the parameter plane. The related stationary equation creates a reversible Hamiltonian system with two degrees of freedom that undergoes the Hamiltonian-Hopf bifurcation with an additional degeneracy. We investigate this bifurcation in a two-parameter unfolding by means of the sixth-order normal form for the related Hamiltonian. The region where no localized solutions exist has been pointed out as well. (c) 1995 American Institute of Physics.
authors.affiliation: Institute of Applied Physics of RAS, 46, Ul'yanov St., Nizhniy Novgorod, 603600 RussiaResearch Institute for Applied Mathematics and Cybernetics, 10, Ul'yanov St., Nizhniy Novgorod, 603600 Russia.
authors.forename: L. Yu.
authors.initials: LY
authors.lastname: Glebsky
authors.forename: L. M.
authors.initials: LM
authors.lastname: Lerman