Abstract
In this chapter, we consider a generalized coupled Boussinesq system of KdV–KdV type, which belongs to the class of Boussinesq systems modeling two-way propagation of long waves of small amplitude on the surface of an ideal fluid. We obtain conservation laws for this system using Noether theorem. Since this system does not have a Lagrangian, we increase the order of the partial differential equations by using the transformations $u={U_{x}}$ , $v={V_{x}}$ and convert the Boussinesq system to a fourth-order system in U, V variables, which has a Lagrangian. Consequently, we find infinitely many nonlocal conserved quantities for our original Boussinesq system of KdV–KdV type.
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