Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3235
Abstract
We analyze three types of integrable nonlinear evolution equations (NLEE) related to the Kac-Moody algebras $A_r^{(1)}$. These are $\mathbb{Z}_h$-reduced derivative NLS equations (DNLS), multicomponent mKdV equations and 2-dimensional Toda field theories (2dTFT). We outline the basic tools of this analysis: i) the gradings of the simple Lie algebras using their Coxeter automorphisms; ii) the construction of the relevant Lax representations; and iii) the spectral properties of the Lax operators and their reduction to Riemann-Hilbert problems. We also formulate the minimal set of scattering data which allow one to recover the asymptotics of the fundamental analytic solutions to $L$ and its potential.
Keywords
Integrable nonlinear evolution equations, graded simple Lie algebras, Kac-Moody algebras, Riemann-Hilbert problems
First Page
1828
Last Page
1844
Recommended Citation
GERDJIKOV, VLADIMIR S.
(2022)
"Nonlinear evolution equations related to Kac-Moody algebras $A_r^{(1)}$: spectral aspects,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 14.
https://doi.org/10.55730/1300-0098.3235
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/14
