New exact solutions and conservation laws of a coupled Kadomtsev–Petviashvili system

• Exact solutions of a new coupled Kadomtsev–Petviashvili system are obtained.
• Lie symmetry method and the (G′/GG′/G)-expansion methods are employed.
• Travelling wave solutions of the underlying system are obtained.
• We also derive the conservation laws of the coupled Kadomtsev–Petviashvili system.

This paper obtains exact solutions of a new coupled Kadomtsev–Petviashvili system, which arises in the analysis of various problems in fluid mechanics, theoretical physics and many scientific applications. Lie symmetry method along with the (G′/G)(G′/G)-expansion method is employed to find the travelling wave solutions of the underlying system. In addition, we derive the conservation laws of the coupled Kadomtsev–Petviashvili system using the multiplier method.