New conservation laws of the Boussinesq and generalized Kadomtsev–Petviashvili equations via homotopy operator

Abstract

According to the tools of linear algebra and calculus of variations, the conservation laws of Boussinesq and generalized Kadomtsev–Petviashvili (gKP) equations are investigated using multipliers and scaling methods. Using the Euler–Lagrange operator, the determining equations are calculated to find the multipliers of Boussinesq equation and the actual density of gKP equation. Then, the flux and density pairs of Boussinesq equation and the corresponding flux of gKP equation are obtained through 2-dimensional homotopy operator.

Keywords

• Boussinesq equation
• gKP equation
• Conversation laws
• Multiplier method
• Scaling method