Article
Ufa Mathematical Journal
Volume 9, Number 4, pp. 97-107
``Quantizations'' of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$
Pavlenko V.A., Suleimanov B.I.
DOI:10.13108/2017-9-4-97
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We study compatible linear evolutional equations with times $s_1$, $s_2$,
which depend from two space variables. These evolution equations are analogues of the non-stationary Schr\"odinger equations determined by the two Hamiltonian
$H^{\frac{7}{2}+1}_{s_k}(s_1,s_2, q_1,q_2, p_1, p_2)$ $(k=1,2)$ of pair compatible Hamilton systems, which can be allowed the method of isomo\-nodromic deformations. We construct the solution of the two evolutional equations in terms of solution corresponding ordinary differential
equations of the method of isomonodrome deformations. In this work we also show that solutions of the two Hamilton systems with Hamiltonians
$H^{\frac{7}{2}+1}_{s_k}$ explicitly set by common solutions of
the Korteweg de Vries equation $u_t+u_{xxx}+uu_x=0$ and of the fifth order ordinary differential equation.