Solutions of Certain Integrable Nonlinear PDEs (Partial Differential Equations) Describing Nonresonant n-Wave Interactions

摘要

The standard equations that describe the nonresonant interaction of N dispersive waves are described and special cases which are integrable by quadratures are considered. The subclass of localized solutions gives rise to a solitonic phenomenology. The class of solutions that are asymptotically finite contains a richer solitonic phenomenology. The analysis is confined to 1+1 dimensions. Generalizations are also presented, including a partially solvable multidimensional extension.