The Lorentz-Invariant Deformation of the Whitham System for the Nonlinear Klein–Gordon Equation

We consider a deformation of the Whitham system for the nonlinear Klein–Gordon equation. This deformation has a Lorentz-invariant form. Using the Lagrangian formalism of the original system, we obtain the first nontrivial correction to the Whitham system in the Lorentz-invariant approach.