The Lorentz - invariant deformation of the Whitham system for the   non-linear Klein-Gordon equation
  We consider the deformation of the Whitham system for the non-linear Klein-Gordon equation having the Lorentz-invariant form. Using the Lagrangian formalism of the initial system we obtain the first non-trivial correction to the Whitham system in the Lorentz-invariant approach. 
A.Ya. Maltsev