Exact plane symmetric solutions of sin-Gordon equations with inherent gravitational fields taken into account

Abstract

We obtain exact self-consistent plane symmetric solutions to systems of Einstein equations and nonlinear scalar field equations of sin-Gordon type. We write out, in explicit from, two specific solutions corresponding to specific choices of the nonlinearity parameter λ. We show that for each value of λ, there exist solutions of soliton and antisoliton type with topological charge Q=±1. We establish that the basic difference between the solutions we obtain and solutions of the sin-Gordon equation in flat space—time is that when we take internal gravitational fields into account, each value of λ corresponds to a specific function ϕ_λ(x).