The Huygens' property is exploited to study propagation relations for solutions of certain types of linear higher order Cauchy problems. Motivated by the solution properties of the abstract wave problem, addition formulas are developed for the solution operators of these problems. The application of these alternative forms of the solution operators to data leads to connecting operator relations...

We study the higher-order nonlinear dispersive equation ∂tu+ ∂ 2j+1 x u = ∑ 0≤j1+j2≤2j aj1,j2∂ j1 x u∂ j2 x u, x, t ∈ R. where u is a real(or complex-) valued function. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when a0,k 6= 0 for some k > j, in the sense that this equation cann...

For rule validation there are no second and higher order refinement heuristics yet. This paper presents an example for second order refinement heuristics and introduces generic higher order refinement heuristics. It is proposed that rule refinement should be performed case-based, i.e. the whole spectrum from first order to higher order refinement heuristics can be processed instead of first ord...