Nonlinear self-adjointness, conservation laws, exact solutions of a system of dispersive evolution equations

• The nonlinear self-adjointness of a system of dispersive evolution equations is proved.
• The conservation laws associated to their Lie symmetries are established.
• Exact solutions via conservation laws are obtained.

In this paper, we classify a (1+1)(1+1)-dimensional nonlinear system of dispersive evolution equations both from point of view of symmetries and nonlinear self-adjointness. Then, conservation laws are established from the property of nonlinear self-adjointness and from these we obtain exact solutions.