Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system

Lie symmetry analysis is performed on a new coupled KdV system, which arises in the analysis of various problems in theoretical physics and many scientific applications. The similarity reductions and new exact solutions are obtained. The solutions obtained include the solitary waves, cnoidal and snoidal waves. In addition, we derive the conservation laws of the coupled KdV system.

► Lie symmetry analysis is performed on a new coupled KdV system.
► The similarity reductions and new exact solutions are obtained.
► The solutions obtained include the solitary waves, cnoidal and snoidal waves.
► In addition, we derive the conservation laws of the coupled KdV system.