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pro vyhledávání: '"Nikolaev, Nikita"'
Autor:
Nikolaev, Nikita
We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a discrete subset
Externí odkaz:
http://arxiv.org/abs/2410.17224
Autor:
Nikolaev, Nikita
We investigate singularly perturbed nonlinear complex differential systems of the form $\hbar \partial_x f = F (x, \hbar, f)$ where $\hbar$ is a small complex perturbation parameter. Under a geometric assumption on the eigenvalues of the Jacobian mat
Externí odkaz:
http://arxiv.org/abs/2201.04526
Autor:
Nikolaev, Nikita
We prove an Asymptotic Implicit Function Theorem in the setting of Gevrey asymptotics with respect to a parameter. The unique implicitly defined solution admits a Gevrey asymptotic expansion and furthermore it is the Borel resummation of the correspo
Externí odkaz:
http://arxiv.org/abs/2112.08792
Autor:
Nikolaev, Nikita
Publikováno v:
Commun. Math. Phys. 400 (2023) 463-517
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably, our resul
Externí odkaz:
http://arxiv.org/abs/2106.10248
Autor:
Nikolaev, Nikita, Isakova, Victoria, Vnukova, Natalia, Еlesina, Victoria, Glushenko, Gariy, Tomashevich, Yevgeny, Churilov, Grigory
Publikováno v:
In Diamond & Related Materials February 2024 142
Autor:
Nikolaev, Nikita
Publikováno v:
Nagoya Mathematical Journal 250 (2023) 434-469
The singularly perturbed Riccati equation is the first-order nonlinear ODE $\hbar \partial_x f = af^2 + bf + c$ in the complex domain where $\hbar$ is a small complex parameter. We prove an existence and uniqueness theorem for exact solutions with pr
Externí odkaz:
http://arxiv.org/abs/2008.06492
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Autor:
Nikolaev, Nikita
We study singularly perturbed linear systems of rank two of ordinary differential equations of the form $\hbar x\partial_x \psi (x, \hbar) + A (x, \hbar) \psi (x, \hbar) = 0$, with a regular singularity at $x = 0$, and with a fixed asymptotic regular
Externí odkaz:
http://arxiv.org/abs/1909.04011
Autor:
Nikolaev, Nikita
Publikováno v:
Sel. Math. New Ser. 27, 78 (2021)
We prove a functorial correspondence between a category of logarithmic $\mathfrak{sl}_2$-connections on a curve $X$ with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover $\pi : \Sigma \t
Externí odkaz:
http://arxiv.org/abs/1902.03384
Autor:
Vnukova, Natalia G., Nikolaev, Nikita S., Bartseva, Lyubov S., Kastiuk, Maria R., Elesina, Victoria I., Isakova, Victoria G., Churilov, Grigory N.
Publikováno v:
Fullerenes, Nanotubes & Carbon Nanostructures; 2024, Vol. 32 Issue 9, p846-850, 5p