Vahagn Manukian

e-mail: manukive@muohio.edu
  
phone: (513) 785 3220

Education

M.A.   SUNY at Buffalo  

Ph.D. Ohio State University

Positions Held


Aug 2018-Aug 2024
Chair
Department of Mathematical and Physical Sciences, Miami University
Feb 2024-Aug 2024 
Interim Chair
Department of Engineering Technology, Miami University
Aug 2017-Present
Associate Professor
Department of Mathematical and Physical Science, Miami University
Department of Mathematics, Miami University
Aug. 2010-Aug 2017
Assistant Professor
Department of Mathematics, Miami University
Aug. 2008 - May 2010
Lecturer
Department of Mathematics, University of Kansas
June 2005 - Aug. 2008
Postdoctoral Research Associate
Department of Mathematics, University of North Carolina at Chapel Hill
June 2005 - May 2008
Postdoctoral Fellow
Department of Mathematics, North Carolina State University

     Professional Affiliations

  • Adjunct Professor of Mathematics, Associate Member in Graduate Faculty, Department of Mathematics, North Carolina State University; 2013-2018.

  • Long Term Visitor at Institute of Mathematics and its Applications (IMA); June 01, 2013-June 20, 2013.

    Research Interest

  • Homoclinic, heteroclinic and limit cycle bifurcations
  • Existence and stability of nonlinear waves

    

Book

Ghazaryan, S. Lafortune, V. Manukian. Introduction to Traveling Waves, Chapman and Hall/CRC; 1st edition (November 14, 2022).


Publications and Preprints

(* Denotes undergraduate student coauthors; ** Denotes graduate student coauthors.)

A. Ghazaryan, V. Manukian, J. Waldmann*, P. Yinzime**, Regime dependent infection propagation fronts in an SIS model. Quarterly of Applied Mathematics 2025, (Accepted)


A. Ghazaryan, S. Lafortune, Y. Latushkin, V. Manukian, Stability of fronts in the diffusive Rosenzweig-MacArthur model.  Stud Appl Math. 2024; e12755.


V. Manukian, S. Schecter, More traveling waves in the Holling-Tanner model with weak diffusion. Discrete Contin. Dyn. Syst. Ser. B 27 (2022), no. 9,M.


Bakhshi**, A. Ghazaryan, V. Manukian, N. Rodriguez, Traveling wave solutions in a model for social outbursts in a tension-inhibitive regime. Stud. Appl. Math. 147 (2021), no. 2, 650-674.


Ghazaryan, S. Lafortune, V. Manukian, Spectral analysis of fronts in a Marangoni-driven thin liquid film flow down a slope. SIAM J. Appl. Math, Vol. 80, No. 1 (2020) 95-118. 


H. Cai*, A. Ghazaryan, V. Manukian, Fisher-KPP dynamics in diffusive Rosenzweig-MacArthur and Holling-Tanner models. Math. Model. Nat. Phenom. 14 (2019) 404


A. Ghazaryan, S. Lafortune, V. Manukian, Stability of nonlinear waves and patterns and related topics. Phil. Trans. R. Soc. A 376: 2018 0001


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.


A. Ghazaryan, V. Manukian, S. Schecter, Traveling waves in the Holling-Tanner model with weak diffusion. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 471 (2015) 16pp.


V. Manukian, On traveling waves of Gray-Scott model. Dynamical Systems: An International Journal 30 no 3 (2015) 270-296.


A. Ghazaryan, V. Manukian, Coherent structures in a population model for mussel-algae interaction. SIAM Journal on Dynamical Systems 14, no. 2 (2015) 893-913.


N. Costanzino, V. Manukian, C.K.R.T Jones, Solitary waves of the regularized short pulse and Ostrovsky equations. SIAM J. Math. Anal. 41 (2009) 2088-2106.


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.


V. Manukian, B. Sandstede. Multi-hump pulses in systems with reflection and phase invariance. Journal of Differential Equations 247 (2009) 1886-1898.


V. Manukian, S. Schecter. Traveling waves for a thin liquid film with surfactant on an inclined plane. Nonlinearity 22 (2009) 85-122.

Awards and Funding

NSF DMS award 1919555 " Fall 2023 Mathematics Conference: Differential Equations and Dynamical Systems and Applications " $14,880. Co-PI with A. Ghazaryan, Alin Pogan and Alim Sukhtayev. Oxford, Ohio.
NSF  DMS award 1919555 " Fall 2019 Mathematics Conference: Differential Equations and Dynamical Systems and Applications" $11,552.  Co-PI with A. Ghazaryan, Alin Pogan and Alim Sukhtayev. Oxford, Ohio.
Collaboration Grant for Mathematicians from Simons Foundation $35,000. Duration 09/1/2012 -08/31/2018. Project title: Existence and stability of traveling waves.

NSF DMS award 1630812 "Fall 2016 Mathematics Conference: Differential Equations and Dynamical Systems" $10,000.  Co-PI with A. Ghazaryan and Alin Pogan. Oxford, Ohio.
$2700 award from Institute for Mathematics and its Applications (IMA) to visit the IMA from June 01, 2013-June 31, 2013.

Faculty Research Grant, Miami University. Summer 2011.