Abstract
The conservation laws for the variant Boussinesq system are derived by an interesting method of increasing the order of partial differential equations. The variant Boussinesq system is a third-order system of two partial differential equations. The transformations u → U x , v → V x are used to convert the variant Boussinesq system to a fourth order system in U , V variables. It is interesting that a standard Lagrangian exists for the fourth-order system. Noether’s approach is then used to derive the conservation laws. Finally, the conservation laws are expressed in the variables u , v and they constitute the conservation laws for the third-order variant Boussinesq system. Infinitely many nonlocal conserved quantities are found for the variant Boussinesq system.
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