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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2408.14413 |
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Table des matières:
- In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter $ε^2$ . By employing variational techniques, we establish the existence of solutions for all values of $ε$ and get results on their qualitative properties, including regularity. Additionally, we analyse the behaviour of solutions as $ε {\to} 0$, demonstrating their pointwise convergence to the solution of the problem for $ε = 0$. We establish the uniqueness of this solution modulo translations. Additionally, in the final section, through an appropriate change of scale, we relate this problem and the second Painlevé equation.