Invariant variational principles and conservation laws for some nonlinear partial differential equations with variable coefficients part II

The conservation laws via Noetherʹs theorem have been derived for a coupled system of nonlinear partial differential equations (NLPDEs) which modelling physical phenomena represented by the generalized Korteweg–de Vries equation, the variable coefficients nonlinear Korteweg–de Vries equation and the variable coefficients nonlinear Schrödingerʹs equation. For proving the efficiency of the technique under consideration the stable and unstable nonlinear Schrödingerʹs equations have been examined for the conservation laws.