Conservation laws for third-order variant Boussinesq system

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→Ux,v→Vxu→Ux,v→Vx are used to convert the variant Boussinesq system to a fourth order system in U,VU,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,vu,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.