  Domain wall, wormhole, particlelike, and cosmic string general relativistic
solutions supported by two interacting phantom or ordinary scalar fields with
4th-, 6th-, and 8th-order potentials are studied. Numerical calculations
indicate that regular finite energy solutions exist only for specific values of
two free parameters of the potentials. By solving nonlinear eigenvalue problems
for some fixed sets of values of the free parameters and of boundary
conditions, it is shown that the presence or absence of the solutions depends
on a particular symmetry of the problem, on the type of the scalar fields
(ordinary or phantom), and on the form of the potential.
