### Stefan Mancas

#### Areas of Expertise

1. PDEs: nonlinear evolution equations, water waves, soliton interactions, hydrodynamics and fluid mechanics

2. ODEs: nonlinear dynamical systems, bifurcation theory, integrability of Riccati and Abel equations, special functions

3. Mathematical physics, differential geometry, cosmology and inflation, nonlinear optics

#### External Links

*The views expressed on faculty and external web pages are those of the author and do not necessarily represent those of Embry-Riddle Aeronautical University.*

#### Biography

I received a Ph.D. in Applied Mathematics from the University of Central Florida in May 2007 under the supervision of Dr. Roy S. Choudhury. My dissertation topic was "Dissipative Solitons in the cubic-quintic Complex Ginzburg Landau equation: Bifurcations and Spatiotemporal Structure" for which I received the Outstanding Dissertation Award from UCF in 2008.

My current areas of research activities at Embry-Riddle involve finding analytical solutions to nonlinear evolution equations and dynamical systems. The methods used are based primarily on bifurcation theory for dynamical systems, and techniques involving special functions and complex analysis with applications to water waves, soliton theory, biological systems, cosmology and inflation for evolution equations.

#### Education

- Ph.D. - Doctor of Philosophy in Mathematics, University of Central Florida
- M.S. - Master of Science in Mathematical Science, University of Central Florida
- B.S. - Bachelor of Science in Mathematics, University of Central Florida

#### Currently Teaching

- MA 243: Calculus & Analytical Geom III
- MA 243HON: Calc & Analytical Geometry III

#### Courses Taught

Numerical Methods in Fluids (MA 488/MA 595), Complex Analysis for Engineers (MA

443), Partial Differential Equations for Engineers (MA 442), Numerical Methods for Engineers with

MATLAB (MA 438), Linear Algebra (MA 432), Advanced Engineering Mathematics (MA 441),

Differential Equations (MA 345), Calculus with Analytic Geometry I, II and III (MA 241, MA 242

and MA 243), Analytic Trigonometry (MA 142), College Mathematics for Aviation II (MA 112)

#### Research Projects

#### Publications

1. Adams, R., & Mancas, S. C. (2017). Stability of solitary and cnoidal traveling wave solutions

for a fifth order Korteweg-de Vries equation. Applied Mathematics and Computation.

Accepted

2. Mancas, S. C. (2017). Traveling wave solutions to Kawahara and related equations. Differential

Equations and Dynamical Systems, 1-19. (DOI 10.1007/s12591-017-0367-5). In press.

3. Mancas, S. C., & Adams, R. (2017). Elliptic solutions and solitary waves of a higher order

KdV-BBM long wave equation. Journal of Mathematical Analysis and Applications, 452(2),

1168-1181.

4. Rosu, H. C., & Mancas, S. C. (2017). Generalized Thomas{Fermi equations as the Lampariello

class of Emden-Fowler equations. Physica A: Statistical Mechanics and its Applications, 471,

212-218.

5. Mancas, S. C., & Rosu, H. C. (2016). Integrable Abel equations and Vein's Abel equation.

Mathematical Methods in the Applied Sciences, 39(6), 1376-1387.

6. Mancas, S. C., & Rosu, H. C. (2016). Evolution of spherical cavitation bubbles: Parametric

and closed-form solutions. Physics of Fluids, 28(2), 022009.

7. Reyes, M. A., Gutierrez-Ruiz, D., Mancas, S. C., & Rosu, H. C. (2016). Nongauge bright

soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations.

Modern Physics Letters A, 31(03), 1650020.

8. Mancas, S. C., & Rosu, H. C. (2016). Existence of periodic orbits in nonlinear oscillators of

Emden-Fowler form. Physics Letters A, 380(3), 422-428.

9. Mancas, S. C., Sajjadi, S. G., Anderson, A., & Hoffman, D. (2016). Micro cavitation bubbles

on the movement of an experimental submarine: Theory and Experiments. Advances and

Applications in Fluid Mechanics, 19(1), 169-201.

10. Berard, F., Vandamme, C. J., & Mancas, S. C. (2015). Two-dimensional structures in the

quintic Ginzburg-Landau equation. Nonlinear Dynamics, 81(3), 1413-1433.

11. Rosu, H. C., Mancas, S. C., & Chen, P. (2015). Barotropic FRW cosmologies with Chiellini

damping in comoving time. Modern Physics Letters A, 30(20), 1550100.

12. Mancas, S. C., & Rosu, H. C. (2015). Integrable equations with Ermakov-Pinney nonlinearities

and Chiellini damping. Applied Mathematics and Computation, 259, 1-11.

13. Rosu, H. C., Mancas, S. C., & Chen, P. (2015). Barotropic FRW cosmologies with Chiellini

damping. Physics Letters A, 379(10), 882-887.

14. Rosu, H. C., Mancas, S. C., & Chen, P. (2015). One-parameter supersymmetric Hamiltonians

in momentum space. Physica Scripta, 90(5), 055208.

15. Mancas, S. C., & Choudhury, R. S. (2015). Pulses and snakes in Ginzburg-Landau equation.

Nonlinear Dynamics, 79(1), 549-571.

16. Sajjadi, S. G., Mancas, S. C., & Drullion, F. (2015). Formation of three{dimensional surface

waves on deep water using elliptic solutions of nonlinear Schrodinger equation. Advances and

Applications in Fluid Mechanics, 18(1), 81-112.

17. Mancas, S. C., & Rosu, H. C. (2014). Ermakov-Lewis invariants and Reid systems. Physics

Letters A, 378(30), 2113-2117.

18. Rosu, H. C., Mancas, S. C., & Chen, P. (2014). One-parameter families of supersymmetric

isospectral potentials from Riccati solutions in function composition form. Annals of Physics,

343, 87-102.

19. Rosu, H. C., Mancas, S. C., & Chen, P. (2014). Shifted one-parameter supersymmetric family

of quartic asymmetric double-well potentials. Annals of Physics, 349, 33-42.

20. Mancas, S. C., & Rosu, H. C. (2013). Integrable dissipative nonlinear second order differential

equations via factorizations and Abel equations. Physics Letters A, 377(21), 1434-1438.

21. Mancas, S. C., Spradlin, G., & Khanal, H. (2013). Weierstrass traveling wave solutions for

dissipative Benjamin, Bona, and Mahony (BBM) equation. Journal of Mathematical Physics,

54(8), 081502. (Editor's pick).

22. Mancas, S. C., Khanal, H., & Sajjadi, S. G. (2011). Solitary waves, periodic and elliptic

solutions to the Benjamin, Bona & Mahony (BBM) equation modi ed by viscosity. Advances

and Applications in Fluid Mechanics, 9(1), 1-16

23. Berard, F., & Mancas, S. C. (2010). Spatiotemporal two{dimensional solitons in the complex

Ginzburg-Landau equation. Advances and Applications in Fluid Mechanics, 8(2), 141-156.

24. Mancas, S. C., & Choudhury, R. S. (2009). Snake solitons in the cubic-quintic Ginzburg-

Landau equation. Mathematics and Computers in Simulation, 80(1), 73-82.

25. Mancas, S. C., & Choudhury, S. R. (2009). Spatiotemporal structure of pulsating solitons in

the cubic-quintic Ginzburg-Landau equation: a novel variational formulation. Chaos, Solitons

& Fractals, 40(1), 91-105.

26. Khanal, H., & Mancas, S. C. (2009). Numerical simulations of snake dissipative solitons

in complex cubic-quintic Ginzburg-Landau equation. Advances and Applications in Fluid

Mechanics, 5(2), 197-218.

27. Mancas, S. C., & Choudhury, R. S. (2009). Periodic and chaotic traveling wave patterns

in reaction-diffusion/predator-prey models with general nonlinearities. Far East Journal of

Dynamical Systems, 11(2),117-142.

28. Mancas, S. C., & Choudhury, S. R. (2007). A novel variational approach to pulsating solitons

in the cubic-quintic Ginzburg-Landau equation. Theoretical & Mathematical Physics, 152(2),

1160-1172.

29. Mancas, S. C., & Choudhury, S. R. (2007). Bifurcations of plane wave (CW) solutions in the

complex cubic-quintic Ginzburg-Landau equation. Mathematics and Computers in Simulation,

74(4), 266-280.

30. Mancas, S. C., & Choudhury, S. R. (2007). The complex cubic{quintic Ginzburg-Landau equation:

Hopf bifurcations yielding traveling waves. Mathematics and Computers in Simulation,

74(4), 281-291.

31. Mancas, S. C., & Choudhury, S. R. (2006). Traveling wavetrains in the complex cubic-quintic

Ginzburg-Landau equation. Chaos, Solitons & Fractals, 28(3), 834-843.

32. Mancas, S., & Choudhury, S. R. (2006). Bifurcations and competing coherent structures in

the cubic-quintic Ginzburg-Landau equation I: Plane wave (CW) solutions. Chaos, Solitons

& Fractals, 27(5), 12561-1271.

#### Professional Experience

Embry-Riddle Aeronautical University, Daytona-Beach, USA

Associate Chair Fall 2017 -- present

Associate Professor Fall 2013 -- present

Hochschule Munchen/ Munich University of Applied Sciences, Munich, Germany

UAS7 Research Professor Fellowship Spring 2015 -- Summer 2015

Embry-Riddle Aeronautical University, Daytona-Beach, USA

Assistant Professor Fall 2007 -- Summer 2013

#### Memberships and Credentials

July 2017

2. LeCosPA, Leung Center for Cosmology and Particle Astrophysics, National Taiwan University,

Taipei, December 2014

3. ICTP, International Centre for Theoretical Physics, Summer School on Cosmology, Trieste,

Italy, August 2014

4. IMECC-UNICAMP, Workshop on Nonlinear Dispersive Equations, Institute of Mathematics,

State University of Campinas, Brazil, October 2013

5. IPICyT, Instituto Potosino de Investigation Cientifica y Tecnologica, San Luis Potosi, Mexico,

August 2013

6. Secondary Calculus, Levi-Civita Institute, Dififety School, July 2011

7. Classical and Quantum Integrable Models, EPSRC/ London Mathematical Society, University

of Kent, UK, July 2010

8. Universita degli Studi di Milano, Italy, Dipartimento di Filologia Moderna, Italian language

and culture summer scholarship, May -- July 2006

9. NSF--UCF, 3D Optical Memory, Ecole Normale Superieur, Paris, France, May -- September

2001

#### Awards, Honors and Recognitions

**1. External (funded) (total $104,000)**

#1 MUAS, Hochschule Munchen/Munich University of Applied Sciences -- Visiting Research

Fellowship, March-August 2015, $18,000

#2 GFS Corp, Efficiency of a Diffuser -- CoPI, Summer 2012-2013, $31,000, with A. Ludu (PI)

#3 NASA-FSGC, Florida Space Grant Consortium, Aerodynamic Stability of Satellites

in Elliptic Low Earth Orbits -- PI, Fall 2009 -- Spring 2010, $20,000, with B. Udrea (CoPI)

#4 UCF, Undergraduate to graduate fellowship, Fall 2002 -- Fall 2004, $20,000

#5 NSF, International research fellowship -- College of Optics and Photonics, (CREOL) and Ecole Normale Superieur, Paris, France, May -- August 2001, $15,000

**2. Internal (funded) (total $233,500)**

#1 IGNITE-ERAU, Soliton Ship -- Faculty adviser to build an efficient soliton ship with

Honors College students, Summer 2014, $10,000

#2 ERAU, Nonlinear Waves Lab (NLWL3) -- to build a wave tank 32' x 4' x 4', President's

Office, Spring 2014, $136,000, with A. Ludu

#3 ERAU Faculty Internal Research Award, An Investigation on the Nature of Micro

Cavitation Bubbles on the Movement of Undersea Vessels -- Summer 2013 -- Summer 2014,

$5,500

#4 CNLS-2013, Summer Conference and Summer School -- Kathmandu, Nepal, Summer 2013,

$15,000, with H. Khanal (CoPI)

#5 ERAU, Nonlinear Waves Lab (NLWL2) -- to build a wave tank 16' x 4' x 4' President's

Office, Summer 2011-Summer 2012, $35,000, with A. Ludu

#6 ERAU, Faculty Development Funding, President's Office, Summer 2011, $3,500

#7 ERAU, Educational Technology", March 2011 to develop the Computational Math Lab (LB

120) with 8 Linux computers, and expanded later to 15 Linux computers in COAS 301.39,

$10,500

#8 ERAU Faculty Internal Research Award, Chaotical and Erupting Solitons in the

Ginzburg--Landau Equation -- July 2009 -- June 2010, $7,500

#9 ERAU Faculty Internal Research Award, Spatiotemporal Structure of Dissipative Solitons

in the cubic--quintic Ginzburg--Landau equation -- July 2008 -- June 2009, $10,500