RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2013

 / 

July

←  →

Methodological notes


Nonlinear dynamics of quadratically cubic systems

 a, b, c, d, e
a Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
b Prokhorov General Physics Institute of the Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991, Russian Federation
c Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Bolshaya Gruzinskaya ul. 10, Moscow, 123995, Russian Federation
d N.I. Lobachevskii Nizhnii Novgorod State University, prosp. Gagarina 23, Nizhnii Novgorod, Russian Federation
e Blekinge Institute of Technology, Karlskrona, Sweden

A modified form of the known nonlinear dynamics equations is proposed which uses quadratic relations to model cubic nonlinearity. It is shown that such quadratically cubic equations are sometimes amenable to exact solutions and that sometimes they make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and nonlinear partial differential equations of the Hopf, Burgers, Korteveg—de Vries, and Schrödinger types. Some problems are solved exactly in the spatiotemporal and spectral representations. The unsolved problems potentially amenable to the proposed approach are listed.

Fulltext pdf (536 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0183.201307b.0719
PACS: 02.30.Jr, 05.45.−a, 42.65.−k, 43.25.+y (all)
DOI: 10.3367/UFNe.0183.201307b.0719
URL: https://ufn.ru/en/articles/2013/7/b/
000325716100002
2-s2.0-84885986245
2013PhyU...56..683R
Citation: Rudenko O V "Nonlinear dynamics of quadratically cubic systems" Phys. Usp. 56 683–690 (2013)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 9th, April 2013, revised: 29th, April 2013, 9th, April 2013

Оригинал: Руденко О В «Нелинейная динамика квадратично кубичных систем» УФН 183 719–726 (2013); DOI: 10.3367/UFNr.0183.201307b.0719

References (24) Cited by (19) ↓ Similar articles (20)

  1. Pelinovsky E, Talipova T, Didenkulova E Physics Letters A 507 129489 (2024)
  2. Bulatov P E, Cheng H et al Theor Math Phys 220 1097 (2024)
  3. Slunyaev A V, Kokorina A V, Pelinovsky E N Communications In Nonlinear Science And Numerical Simulation 127 107527 (2023)
  4. Nefedov N, Polezhaeva E, Levashova N Axioms 12 253 (2023)
  5. Pelinovsky D E, Slunyaev A V et al Communications In Nonlinear Science And Numerical Simulation 101 105855 (2021)
  6. Pelinovsky E, Talipova T, Soomere T Physica D: Nonlinear Phenomena 419 132785 (2021)
  7. Nazarov V E, Kiyashko S B Radiophys Quantum El 64 332 (2021)
  8. Rudenko O V, Hedberg C M Wave Motion 89 104 (2019)
  9. Andreev V G, Gramovich V V et al Acoust. Phys. 65 765 (2019)
  10. Vasil’eva O A, Lapshin E A, Rudenko O V Acoust. Phys. 65 23 (2019)
  11. Rudenko O V, Hedberg C M, Ibragimov R N Math. Model. Nat. Phenom. 13 18 (2018)
  12. Rudenko O V Dokl. Math. 96 399 (2017)
  13. Rudenko O V Dokl. Math. 94 708 (2016)
  14. Dubkov A A, Rudenko O V, Gurbatov S N Phys. Rev. E 93 (6) (2016)
  15. Rudenko O V, Hedberg C M Nonlinear Dyn 85 767 (2016)
  16. Rudenko O V Dokl. Math. 94 468 (2016)
  17. Gurbatov S N, Rudenko O V Radiophys Quantum El 58 463 (2015)
  18. Rudenko O V Bull. Russ. Acad. Sci. Phys. 79 1215 (2015)
  19. Nikitenkova S, Pelinovsky E Abstract And Applied Analysis 2014 1 (2014)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions