Exponentially fitted methods that preserve conservation laws

The exponential fitting technique uses information on the expected behaviour of solution a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when applied problems with oscillatory solutions. this cases, compared standard methods, they have proved be even using large integration steps. paper we consider Runge-Kutta give characterizations those that preserve local conservation laws linear quadratic quantities. As benchmark wave equations arising as models in several fields such fluid dynamics quantum physics, derive their mass (or charge) momentum. proposed approximate breather solutions other known same order.