Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

Abstract A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is coupled Schrödinger and wave equation with non-dispersive direction. In this paper, new local well-posedness result rough initial data established. The proof based on an efficient use smoothing maximal function norms.

The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference operators. Polynomial differential operators case is investigated. Covariant sets of potentials are introduced by a periodic chain closure. The symmetry of the syste...

We consider the Zakharov-Kuznestov (ZK) equation posed in a limited domain M = (0, 1)x × (−π/2, π/2)d, d = 1, 2 supplemented with suitable boundary conditions. We prove that there exists a solution u ∈ C([0, T ];H1(M)) to the initial and boundary value problem for the ZK equation in both dimensions 2 and 3 for every T > 0. To the best of our knowledge, this is the first result of the global exi...