Multisymplectic relative equilibria, multiphase wavetrains, and coupled NLS equations

摘要

The article begins with a geometric formulation of two-phase wavetrain solutions of coupled nonlinear Schrodinger equations. It is shown that these solutions come in natural four-parameter families, associated with symmetry, and a geometric instability condition can be deduced from the parameter structure that generalizes Roskes' instability criterion. It is then shown that this geometric structure is universal in the sense that it does not depend on the particular equation; only on the structure of the equations. The theory also extends to the case without symmetry, where small divisors may be present, but gives a new formal geometric framework for multiphase wavetrains. [References: 13]