'Quantization' of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom
| Autor: | Suleimanov, Bulat |
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| Jazyk: | ruština |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Functional Analysis and Its Applications, 2014, 48: 3, 198-207 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4213/faa3150 |
| Popis: | We construct a solution of an analog of the Schr\"{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. This solution is produced by an explicit change of variables from a solution of the linear equations whose compatibility condition is the ordinary differential equation $P_1^2$ with respect to $z$. This solution also satisfies an analog of the Schr\"{o}dinger equation corresponding to the Hamiltonian $ H_{II} (z, t, q_1, q_2, p_1, p_2) $ of Hamiltonian system with respect to $t$ which is compatible with $P_1^2$. A similar situation occurs for the $P_2^2$ equation in the Painleve II hierarchy. Comment: 13 pages, in Russian. There is an English translation of the text containing misprints in the formula (5), (19) and in the first equation of the concluding observations |
| Databáze: | arXiv |
| Externí odkaz: |
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