Analysis reveals multi-bubble solutions exist in Liouville systems on a flat torus, highlighting new matrix properties.
We study the following Liouville system defined on a flat torus where , , and is doubly periodic on . The matrix satisfies certain properties. One central problem about Liouville systems is whether multi‐bubble solutions do exist. In this work we present a comprehensive construction of multi‐bubble solutions in the most general setting.
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Cheng et al. (2025) studied this question.
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