Conservation laws for a Boussinesq equation.

Abstract

In this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential equation, we obtain directly a second order ordinary differential equation and two third order ordinary differential equations.

Keywords

• generalized boussinesq equation
• conservation laws
• potential symmetries
• double reduction
• 35q35
• 76m60
• 58j45