Connection formulae for the radial Toda equations II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916589077528576 |
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| author | Guest, Martin A. Its, Alexander R. Kosmakov, Maksim Miyahara, Kenta Odoi, Ryosuke |
| author_facet | Guest, Martin A. Its, Alexander R. Kosmakov, Maksim Miyahara, Kenta Odoi, Ryosuke |
| contents | This is a continuation of [arXiv:2309.16550] in which we computed the asymptotics near $x = \infty$ of all solutions of the radial Toda equation. In this article, we compute the asymptotics near $x = \infty$ of all solutions of a "partner" equation. The equations are related in the sense that their respective monodromy data constitute connected components of the same "monodromy manifold". While all solutions of the radial Toda equation are smooth, those of the partner equation have infinitely many singularities, and this makes the Riemann-Hilbert nonlinear steepest descent method (and the asymptotics of solutions) more involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connection formulae for the radial Toda equations II Guest, Martin A. Its, Alexander R. Kosmakov, Maksim Miyahara, Kenta Odoi, Ryosuke Mathematical Physics Classical Analysis and ODEs This is a continuation of [arXiv:2309.16550] in which we computed the asymptotics near $x = \infty$ of all solutions of the radial Toda equation. In this article, we compute the asymptotics near $x = \infty$ of all solutions of a "partner" equation. The equations are related in the sense that their respective monodromy data constitute connected components of the same "monodromy manifold". While all solutions of the radial Toda equation are smooth, those of the partner equation have infinitely many singularities, and this makes the Riemann-Hilbert nonlinear steepest descent method (and the asymptotics of solutions) more involved. |
| title | Connection formulae for the radial Toda equations II |
| topic | Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.17783 |