Nikita Nikolaev

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20192026

most citedExistence and Uniqueness of Exact WKB Solutions for Second-Order Singularly Perturbed Linear ODEs

16 citations · 39 across the 10 of their papers we have counts for

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math.CA2022

An Exact Perturbative Existence and Uniqueness Theorem

Nikita Nikolaev

We investigate singularly perturbed nonlinear complex differential systems of the form $ℏ \partial_{x} f = F (x, ℏ, f)$ where $ℏ$ is a small complex perturbation paramete…

math.CA2020★ 16 cited

Exact Solutions for the Singularly Perturbed Riccati Equation and Exact WKB Analysis

Nikita Nikolaev

The singularly perturbed Riccati equation is the first-order nonlinear ODE $ℏ \partial_{x} f = a f^{2} + b f + c$ in the complex domain where $ℏ$ is a small complex parameter. We…

math.CA2019

Triangularisation of Singularly Perturbed Logarithmic Differential Systems of Rank 2

Nikita Nikolaev

We study singularly perturbed linear systems of rank two of ordinary differential equations of the form $ℏ x \partial_{x} ψ (x, ℏ) + A (x, ℏ) ψ (x, ℏ) = 0$ , with a regul…