New solutions for difference-difference models of the φ4 equation and nonlinear Klein-Gordon equation in 1 + 1 dimension

We present a new solution for Hirotaʹs difference-difference model of the φ4 equation in 1 + 1 dimension, extending Hirotaʹs kink solution. We also present three new solutions for a difference-difference model of the nonlinear Klein-Gordon equation. We discuss asymptotic behaviours of these solutions in small limits of the lattice spacing.