On small stationary localized solutions for the generalized 1-D Swift-Hohenberg equation.
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.
Glebsky
L. Yu.
LY
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.
Lerman
L. M.
LM