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Approximate solutions for the skyrmion

J. A. Ponciano·L. N. Epele·H. Fanchiotti·C. A. Garcia Canal
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Abstract

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 Pade 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 2-point Pade approximant procedure whereby the exact behaviour 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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J. A. Ponciano, L. N. Epele, H. Fanchiotti, C. A. Garcia Canal. 2001-06-25. Approximate solutions for the skyrmion. https://doi.org/10.1103/physrevc.64.045205

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