Conservation laws for a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model

We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws.

► The Lie point symmetries of a particular case of the CVmkdV system are found.
► The quasi self-adjoint property of the system is shown.
► Conservation laws using the found Lie point symmetries are constructed.