The existence of many periodic non-travelling solutions to the Boussinesq equation

This paper uses variational methods-in particular, a generalization of the Mountain Pass Lemma of Rabinowitz-together with an invariance argument to demonstrate the existence of (weak Sobolev) periodic, non-travelling solutions to the Boussinesq equation partial derivative(2)u/partial derivative t(2) - partial derivative(2)u/partial derivative x(2) - gamma partial derivative(4)u/partial derivative x(4) - g(1) (u, partial derivative u/partial derivative x) - partial derivative/partial derivative x g(2) (u, partial derivative u/partial derivative x) = 0. In certain cases, the author demonstrates the existence of infinitely-many such solutions. The assumptions on the non-linear terms are that they are odd and roughly polynomial, and that they satisfy del G = (g(1), -g(2)) for some G is an element of C-2(R(2); R). (C) 1996 Academic Press, Inc.