Multisymplectic relative equilibria, multiphase wavetrains, and coupled NLS equations

The article begins with a geometric formulation of two-phase wavetrain solu tions of coupled nonlinear Schrodinger equations. It is shown that these so lutions come in natural four-parameter families, associated with symmetry, and a geometric instability condition can be deduced from the parameter str ucture that generalizes Roskes' instability criterion. It is then shown tha t this geometric structure is universal in the sense that it does not depen d on the particular equation; only on the structure of the equations. The t heory also extends to the case without symmetry, where small divisors may b e present, but gives a new formal geometric framework for multiphase wavetr ains.