Similarity inner solutions for the Pulsar equation |
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Authors: | Andronikos Paliathanasis |
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Institution: | Institute of Systems Science, Durban University of Technology, Durban, Republic of South Africa |
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Abstract: | Lie symmetries are applied to classify the source of the magnetic field for the Pulsar equation near to the surface of the neutron star. We find that there are six possible different admitted Lie algebras. We apply the corresponding Lie invariants to reduce the Pulsar equation close to the surface to an ordinary differential equation. This equation is solved either with the use of Lie symmetries or the application of the ARS algorithm for singularity analysis to write the analytic solution as a Laurent expansion. These solutions are called inner solutions. |
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Keywords: | Pulsar equation second-order elliptic equations similarity solutions singularity analysis symmetries symmetry analysis |
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