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The symmetric regularized long wave system (SRLW) is a model for the weaklynonlinear ion acoustic and space-charge waves, which was introduced by C.Seyler and D. Fenstermacher. In this paper, we investigated the wellposednessand controllability properties of the generalized symmetric regularized longwave system (g-SRLW) in different structures (periodic and bounded domains).Firstly, the wellposedness and the exact controllability results for bothlinear and nonlinear g-SRLW system posed on the one-dimensional torus areobtained under the effect of a distributed moving control. Second, we considerthe g-SRLW system in a bounded interval with some Dirichlet-Neumann conditionsand we show that the system is not spectrally controllable (No finite linearcombination of eigenfunctions associated with the state equations, other thanzero, can be steered to zero). Although the system is not spectrallycontrollable, it can be shown that it is approximately controllable.

The Well-posedness and Controllability of the Generalized Symmetric Regularized Long Wave System