Russian Physics Journal

, Volume 39, Issue 10, pp 977–983 | Cite as

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

  • G. N. Shikin
Physics of Elementary Particles and Field Theory


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 ϕλ(x).


Soliton Scalar Field Gravitational Field Einstein Equation Nonlinearity Parameter 
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  1. 1.
    E. Kamke, Handbook of Ordinary Differential Equations [Russian translation], Nauka, Moscow (1965).Google Scholar
  2. 2.
    R. Rajarami, Solitons and Instantons in Quantum Field Theory [Russian translation], Mir, Moscow (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • G. N. Shikin

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