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arXiv · 2506.05547

On the orbital stability of periodic snoidal waves for the $\phi^4-$equation

B. S. Lonardoni·F. Natali
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Abstract

The main purpose of this paper is to investigate the global well-posedness and orbital stability of odd periodic traveling waves for the $\phi^4$-equation in the Sobolev space of periodic functions with zero mean. We establish new results on the global well-posedness of weak solutions by combining a semigroup approach with energy estimates. As a consequence, we prove the orbital stability of odd periodic waves by applying a Morse index theorem to the constrained linearized operator defined in the Sobolev space with the zero mean property.

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B. S. Lonardoni, F. Natali. 2025-06-05. On the orbital stability of periodic snoidal waves for the $\phi^4-$equation. https://arxiv.org/abs/2506.05547

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