hey!

Wave is something which carries energy and propagates with disturbance. The waves which need medium to propagate are called mechanical waves. And the waves which do not require any medium ,and are created by the variations in electric and magnetic field are called electromagnetic waves. these are also called solutions of maxwell's equations. You can check out the equations and derivations here:

https://learn.careers360.com/physics/electromagnetic-waves-chapter/

Thankyou