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[formula]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 G=(g1, −g2) for someG C2(R2; R).