Approximate solutions for the skyrmion
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pad\'e approximants are we...
Guardado en:
| Autores principales: | , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2001
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/125900 |
| Aporte de: |
| Sumario: | We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pad\'e approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the two-point Pad\'e approximant procedure whereby the exact behavior at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r. |
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