Marcelo Cavalcanti, Wellington Correa, Mauricio Sepúlveda, Rodrigo Véjar:
Well-posedness, exponential decay estimate and numerical results for the high order nonlinear Schrödinger equation with localized dissipation
In this work, we study the existence at the L2 - level as well as the stability for the high order nonlinear Schrödinger equation in a bounded interval with a localized damping term. To prove the existence, we employ a method devised by Bisognin et al. To prove the exponential stabilization with these approximations, we use multipliers techniques found in the same reference and in other paper by Linares and Pazoto. In addition, we implement a precise and efficient code to study the energy decay of the high order nonlinear Schrödinger equation.