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

Abstract

AbstractConsider 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.