| Abstract: |
| The linearized eigenvalue problems for stationary solutions of the 1-dimensional reaction-diffusion
equations are considered. In the previous studies by the author, expressions of all eigenfunctions in terms of the Jacobi elliptic functions are obtained for typical cases of the bistable nonlinearity. We will show the recent results on the expressions of linearized eigenvalue problems for the other cases of nonlinearity. In particular, we will introduce the modified elliptic intergral of the third kind, which appear in the characteristic equations of eigenvalues for these cases of nonlinearity. We will also focus on the relationship with the Lam'e equation. |
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