Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zapiski Nauchnykh Seminarov POMI, 2023, Volume 520, Pages 189–226 (Mi znsl7318)  

One-parameter meromorphic solution of the degenerate third Painlevé equation with formal monodromy parameter $a=\pm\mathrm{i}/2$ vanishing at the origin

A. V. Kitaeva, A. Vartanianb

a Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
b Department of Mathematics, College of Charleston, Charleston, SC 29424, USA
References:
Abstract: We prove that there exists a one-parameter family of meromorphic solutions $u(\tau)$ vanishing at $\tau=0$ of the degenerate third Painlevé equation,
\begin{equation*} u^{\prime \prime}(\tau) = \frac{(u^{\prime}(\tau))^{2}}{u(\tau)} - \frac{u^{\prime}(\tau)}{\tau} + \frac{1}{\tau} \left(-8 \varepsilon (u(\tau))^{2} + 2ab \right) + \frac{b^{2}}{u(\tau)},\ \varepsilon=\pm1,\ \varepsilon b>0, \end{equation*}
for formal monodromy parameter $a=\pm\mathrm{i}/2$. We study number-theoretic properties of the coefficients of the Taylor-series expansion of $u(\tau)$ at $\tau=0$ and its asymptotic behaviour as $\tau\to+\infty$. These asymptotics are visualized for generic initial data.
Key words and phrases: Painlevé equation, monodromy data, asymptotics, content of polynomial.
Received: 26.05.2023
Document Type: Article
UDC: 517
Language: English
Citation: A. V. Kitaev, A. Vartanian, “One-parameter meromorphic solution of the degenerate third Painlevé equation with formal monodromy parameter $a=\pm\mathrm{i}/2$ vanishing at the origin”, Questions of quantum field theory and statistical physics. Part 29, Zap. Nauchn. Sem. POMI, 520, POMI, St. Petersburg, 2023, 189–226
Citation in format AMSBIB
\Bibitem{KitVar23}
\by A.~V.~Kitaev, A.~Vartanian
\paper One-parameter meromorphic solution of the degenerate third Painlev\'e equation with formal monodromy parameter $a=\pm\mathrm{i}/2$ vanishing at the origin
\inbook Questions of quantum field theory and statistical physics. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 520
\pages 189--226
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7318}
Linking options:
  • https://www.mathnet.ru/eng/znsl7318
  • https://www.mathnet.ru/eng/znsl/v520/p189
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:41
    Full-text PDF :25
    References:23
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024