New static solutions of symmetric ${\varphi }^4$ equation

Abstract

In this paper, we provide new exact solutions of nonlinear Klein-Gordon (${\varphi }^4$) equation in $1+1$-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric ${\varphi }^4$ equation has played an important role in several areas of physics. We obtain several novel non-singular solutions of the symmetric ${\varphi }^4$ model in terms of the Jacobi elliptic functions and compare them with the well-known solutions. Finally, we categorize these solutions in terms of the potential parameters.

11 pages, 5 figures

References in corpus (1)

• Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations