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By using the function and equation transformations,a coupled linear second-order differential equations are reduced to a nonlinear first-order Elliptic equation. And the analytical solutions to coupled transformations that include first-order and second-order transformations are given.The special approximate solution to a superconductivity question derived from a reference is reformed by using the new result given in this paper, and the existence of electric field in the surface of superconductor is validated.
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Keywords:
- differential equations /
- Jacobi elliptic equations /
- analytical solution /
- superconductivity
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