Dark Parameterizations,Equivalent Partner Fields and Integrable Systems

After introducing dark parameters into the traditional physical models, some types of new phenomena may be found. An important difficult problem is how to directly observe this kind of physical phenomena. An alternative treatment is to introduce equivalent multiple partner fields. If use this ideal to integrable systems, one may obtain infinitely many new coupled integrable systemsconstituted by the original usual field and partner fields. The idea is illustrated via the celebrate KdV equation. From the procedure, some byproducts can be obtained: A new method to find exact solutions of some types of coupled nonlinear physical problems, say, the perturbation KdV systems, is provided; Some new localized modes such as the staggered modes can be found and some new interaction phenomena like the ghost interaction are discovered.