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arXiv · 2602.04777

Blow-up Solutions for General Toda Systems on Riemann Surfaces

Zhengni Hu·Miaomiao Zhu
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Abstract

In this paper, we study general Toda systems with homogeneous Neumann boundary conditions on Riemann surfaces. Assuming the surface satisfies the ``$k$-symmetric'' condition, we construct a family of bubbling solutions using singular perturbation methods, where the concentration rates of different components occur in distinct orders. In particular, we establish the existence of asymmetric blow-up solutions for the $SU(3)$ Toda system. Furthermore, the blow-up points are precisely located at the ``$k$-symmetric'' centers of the surface. Keywords: Toda system, Neumann boundary condition, Blow-up solutions, $k$-symmetry, Finite-dimensional reduction

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Zhengni Hu, Miaomiao Zhu. 2026-02-04. Blow-up Solutions for General Toda Systems on Riemann Surfaces. https://doi.org/10.1016/j.jde.2026.114145

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