4 Citations (Scopus)

Abstract

In this paper three-dimensional Klein-Gordon and sine-Gordon equations with a cubic nonlinearity are considered. The exact solution of the nonlinear three-dimensional Klein-Gordon equation is obtained. The dependence of the maximum amplitude on the parameters is studied. The approximate analytical solution for three-dimensional sine-Gordon equation is obtained and the error of solution is determined.

Original languageEnglish
Pages (from-to)611-622
Number of pages12
JournalInternational Journal of Mathematical Analysis
Volume10
Issue number13-16
DOIs
Publication statusPublished - 1 Jan 2016

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Klein-Gordon Equation
Sine-Gordon Equation
Nonlinearity
Three-dimensional
Analytical Solution
Exact Solution

Scopus subject areas

  • Mathematics(all)

Cite this

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title = "On the three-dimensional Klein-Gordon equation with a cubic nonlinearity",
abstract = "In this paper three-dimensional Klein-Gordon and sine-Gordon equations with a cubic nonlinearity are considered. The exact solution of the nonlinear three-dimensional Klein-Gordon equation is obtained. The dependence of the maximum amplitude on the parameters is studied. The approximate analytical solution for three-dimensional sine-Gordon equation is obtained and the error of solution is determined.",
keywords = "Nonlinear klein-gordon equation, Numerical methods, Partial differential equations, Sine-gordon equation",
author = "Kolpak, {Eugeny Petrovich} and Ivanov, {Sergei Evgenievich}",
year = "2016",
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doi = "10.12988/ijma.2016.611",
language = "English",
volume = "10",
pages = "611--622",
journal = "International Journal of Mathematical Analysis",
issn = "1312-8876",
publisher = "Hikari Ltd.",
number = "13-16",

}

On the three-dimensional Klein-Gordon equation with a cubic nonlinearity. / Kolpak, Eugeny Petrovich; Ivanov, Sergei Evgenievich.

In: International Journal of Mathematical Analysis, Vol. 10, No. 13-16, 01.01.2016, p. 611-622.

Research output

TY - JOUR

T1 - On the three-dimensional Klein-Gordon equation with a cubic nonlinearity

AU - Kolpak, Eugeny Petrovich

AU - Ivanov, Sergei Evgenievich

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper three-dimensional Klein-Gordon and sine-Gordon equations with a cubic nonlinearity are considered. The exact solution of the nonlinear three-dimensional Klein-Gordon equation is obtained. The dependence of the maximum amplitude on the parameters is studied. The approximate analytical solution for three-dimensional sine-Gordon equation is obtained and the error of solution is determined.

AB - In this paper three-dimensional Klein-Gordon and sine-Gordon equations with a cubic nonlinearity are considered. The exact solution of the nonlinear three-dimensional Klein-Gordon equation is obtained. The dependence of the maximum amplitude on the parameters is studied. The approximate analytical solution for three-dimensional sine-Gordon equation is obtained and the error of solution is determined.

KW - Nonlinear klein-gordon equation

KW - Numerical methods

KW - Partial differential equations

KW - Sine-gordon equation

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EP - 622

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

SN - 1312-8876

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