Research Interests
- Homoclinic, heteroclinic and limit cycle bifurcations
- Existence and stability of nonlinear waves
- Partial and ordinary differential equations
Book
November 14, 2022
A. Ghazaryan, S. Lafortune, V.
Manukian. Introduction
to Traveling Waves. Chapman and Hall/CRC; 1st edition.
Publications and Preprints
* Denotes undergraduate student coauthors; **
denotes graduate student coauthors.
2025
A. Ghazaryan, V. Manukian, J. Waldmann*,
P. Yinzime**, Regime dependent infection propagation
fronts in an SIS model. Quarterly of Applied
Mathematics (Accepted).
2024
A. Ghazaryan, S. Lafortune, Y. Latushkin,
V. Manukian, Stability of fronts in the diffusive
Rosenzweig-MacArthur model. Studies in Applied
Mathematics (2024); e12755.
2022
V. Manukian, S. Schecter, More traveling
waves in the Holling-Tanner model with weak diffusion. Discrete
& Continuous Dynamical Systems – Series B 27
(2022), no. 9.
2021
M. Bakhshi**, A. Ghazaryan, V. Manukian,
N. Rodriguez, Traveling wave solutions in a model for
social outbursts in a tension-inhibitive regime. Studies
in Applied Mathematics 147 (2021), no. 2, 650–674.
2020
A. Ghazaryan, S. Lafortune, V. Manukian,
Spectral analysis of fronts in a Marangoni-driven thin
liquid film flow down a slope. SIAM Journal on
Applied Mathematics 80 (2020), no. 1, 95–118.
2019
H. Cai*, A. Ghazaryan, V. Manukian,
Fisher–KPP dynamics in diffusive Rosenzweig–MacArthur and
Holling–Tanner models. Mathematical Modelling of
Natural Phenomena 14 (2019) 404.
2018
A. Ghazaryan, S. Lafortune, V. Manukian,
Stability of nonlinear waves and patterns and related
topics. Philosophical Transactions of the Royal
Society A 376 (2018) 20180001.
2015
A. Ghazaryan, S. Lafortune, V. Manukian,
Stability of front solutions in a model for a surfactant
driven flow on an inclined plane. Physica D:
Nonlinear Phenomena 307 (2015) 1–13.
2015
A. Ghazaryan, V. Manukian, S. Schecter,
Traveling waves in the Holling–Tanner model with weak
diffusion. Proceedings of the Royal Society A
471 (2015) 16pp.
2015
V. Manukian, On traveling waves of
Gray–Scott model. Dynamical Systems: An International
Journal 30 (2015), no. 3, 270–296.
2015
A. Ghazaryan, V. Manukian, Coherent
structures in a population model for mussel–algae
interaction. SIAM Journal on Dynamical Systems
14 (2015), no. 2, 893–913.
2009
N. Costanzino, V. Manukian, C. K. R. T.
Jones, Solitary waves of the regularized short pulse and
Ostrovsky equations. SIAM Journal on Mathematical
Analysis 41 (2009) 2088–2106.
2009
V. Manukian, N. Costanzino, C. K. R. T.
Jones, B. Sandstede, Existence of multi-pulses of the
regularized short-pulse and Ostrovsky equations. Journal
of Dynamics and Differential Equations 21 (2009)
607–622.
2009
V. Manukian, B. Sandstede, Multi-hump
pulses in systems with reflection and phase invariance. Journal
of Differential Equations 247 (2009) 1886–1898.
2009
V. Manukian, S. Schecter, Traveling waves
for a thin liquid film with surfactant on an inclined
plane. Nonlinearity 22 (2009) 85–122.