Dimensional Reduction of the Action of Non-Abelian Multiwaves

3D supersymmetric nonlinear multiple D$0$-brane action and 4D counterpart of multiple M-wave system

We construct the complete nonlinear action of multiple system in three dimensional type ii superspace which is invariant under rigid spacetime supersymmetry and under local worldline supersymmetry generalizing the of single action.Found is the complete nonlinear action of multiple system in three dimensional type ii superspace which is invariant under rigid spacetime supersymmetry and under local worldline supersymmetry generalizing the of single action.We show that a particular representative of this family of actions can be obtained by dimensional reduction of the action of non-abelian multiwaves (namw), the counterpart of 11d multiple m-wave (m0) action that we have also constructed in this paper.This reduction results in an action with isnonlinear due to the presence of a certain function of the relative motion hamiltonian the counterpart of which enters the 4d namw action linearly.Curiously, the action possesses double supersymmetry also for an arbitrary function.In particular for we find a dynamical system describing the sum of single action and the action of 1d dimensional reduction of the symcoupled to the worldline supergravity induced by the embedding of the center of energy motion into the superspace.