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.
Scopus subject areas
- Nonlinear klein-gordon equation
- Numerical methods
- Partial differential equations
- Sine-gordon equation