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arXiv · 2603.12978

Existence and uniqueness of the global conservative solutions for the generalized Camassa-Holm equation with dual-power nonlinearities

Jian Chen·Xiaoxin Chen·Zhaoyang Yin
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Abstract

In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent semi-linear system, which allows us to establish the global existence of conservative solutions. Furthermore, for a given global conservative solution, we construct some auxiliary variables tailored to its specific structure and demonstrate that they satisfy a semi-linear system with a unique solution, thereby deriving the uniqueness of conservative solutions to the original equation.

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Jian Chen, Xiaoxin Chen, Zhaoyang Yin. 2026-03-13. Existence and uniqueness of the global conservative solutions for the generalized Camassa-Holm equation with dual-power nonlinearities. https://arxiv.org/abs/2603.12978

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