Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation

Abstract

Consider the (1 + l)-dimensional Klein-Gordon equation

$$ \left( {\square - v (x, t)} \right) \phi (x,t) = 0 $$

(13.1)

in some domain Ω ⊂ ℝ², where

$$ \square : = \frac{{\partial ^2 }} {{\partial x^2 }} - \frac{{\partial ^2 }} {{\partial t^2 }}, v and \phi $$

are real-valued functions. We assume that φ is a twice-continuously differentiable function.