Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
E461419
"Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4681202 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations Context triple: [Nikolay Bogolyubov, notableWork, Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations]
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A.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
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B.
On a General Method in Dynamics
"On a General Method in Dynamics" is a foundational 19th-century paper by William Rowan Hamilton that introduced Hamiltonian mechanics, reformulating classical dynamics in terms of generalized coordinates and conjugate momenta.
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C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
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D.
Lyapunov stability theory
Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
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E.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations Target entity description: "Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
-
A.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
-
B.
On a General Method in Dynamics
"On a General Method in Dynamics" is a foundational 19th-century paper by William Rowan Hamilton that introduced Hamiltonian mechanics, reformulating classical dynamics in terms of generalized coordinates and conjugate momenta.
-
C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
Lyapunov stability theory
Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
-
E.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| aim |
to analyze nonlinear oscillatory systems using asymptotic techniques
ⓘ
to provide practical approximation methods for nonlinear problems ⓘ |
| appliesTo |
nonlinear oscillators
ⓘ
ordinary differential equations ⓘ |
| approachType | analytical ⓘ |
| audience |
graduate students in mathematics and physics
ⓘ
researchers in applied mathematics ⓘ |
| author |
Nikolay N. Bogoliubov
NERFINISHED
ⓘ
Yuri A. Mitropolsky NERFINISHED ⓘ |
| contribution |
formalization of asymptotic approaches to nonlinear oscillatory problems
ⓘ
influence on later work in nonlinear oscillation theory ⓘ systematic framework for constructing asymptotic expansions ⓘ |
| emphasizes |
practical computation of approximate solutions
ⓘ
rigorous justification of asymptotic procedures ⓘ |
| field |
applied mathematics
ⓘ
asymptotic analysis ⓘ differential equations ⓘ nonlinear dynamics ⓘ |
| focusesOn |
construction of approximate analytical solutions
ⓘ
methods for weakly nonlinear oscillatory systems ⓘ systematic development of asymptotic techniques ⓘ |
| language | English ⓘ |
| methodIncludes |
averaging methods
ⓘ
multiple‑scale methods ⓘ perturbation expansions ⓘ slowly varying amplitude and phase methods ⓘ |
| originalLanguage | Russian ⓘ |
| relatedTo |
Bogoliubov–Mitropolsky method
NERFINISHED
ⓘ
theory of nonlinear oscillations ⓘ |
| status | classic reference in nonlinear oscillation theory ⓘ |
| topic |
approximate solutions of nonlinear differential equations
ⓘ
asymptotic methods ⓘ nonlinear oscillations ⓘ perturbation theory ⓘ |
| usedIn |
control theory
ⓘ
engineering ⓘ mechanics ⓘ theoretical physics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations Description of subject: "Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Nikolay Bogolyubov
→
notableWork
→
Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
ⓘ