For any \(\mathrm{n}\) number of coupled nonlinear partial
differential equations for spherically symmetric field equations of the typer
\({ }^2\left(\frac{\partial^2 \phi_j}{\partial r^2}-\frac{\partial^2
\phi_j}{\partial t^2}\right)=F \_i(\phi \mathrm{j})\), where \(\mathrm{j}=1,2,
\ldots \mathrm{n}\), are the number of dependent variables and \(\mathrm{F}
\mathrm{i}\left(\phi \_\mathrm{j}\right)\) are any functions of dependent
variables \(\phi_j, \mathrm{j}=1,2, . . \mathrm{n}\). and free of independent
variables \(\mathrm{r}\) and \(\mathrm{t}\) then a similarity variable is found
as \(\mathrm{s}(\mathrm{r}, \mathrm{t})=\mathrm{r}
/\left[\left(r^2-t^2\right)-\kappa t / \tau+\kappa^2 /\left(4
\tau^2\right)\right]\), where \(\kappa\) and \(\tau \neq 0\) are arbitrary
integration constants. Using \(s(r, t)\) above coupled partial differential
equations can be transformed into coupled ordinary differential equations. This
result may reduce lengthy calculations for finding similarity transformations
of coupled partial differential equations. Using this similarity variable two
exact Dyon solutions of spherically symmetric Yang-Mills-Higg's field equations
are found with 'circular functions.' For which known solutions are with
hyperbolic functions.
Author(s) Details
B.V. Baby
3/88, Jadkal Post, Udupi District, Karnataka State -576 233,
India.
Please see the link:- https://doi.org/10.9734/bpi/rumcs/v9/607
