Stefani Mancas

Title
Professor
Department
Mathematics Department
College
College of Arts & Sciences

Areas of Expertise

1. Mathematical Physics: quantum mechanics, fractional derivatives, general relativity, differential geometry, cosmology and inflation

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

3. PDEs: nonlinear evolution equations, soliton interactions, nonlinear waves, nonlinear optics

Stefani Mancas
​Stefani’s main research areas are finding analytical solutions to nonlinear dissipative equations that can be reduced through Darboux transformations to Riccati or Abel equations. The focus is on Schrödinger equation, for which Stefani is using methods based on factorization, and variational formulation together with ansatz reduction with global minimizers of objective functions, applied to supersymmetric quantum mechanics. Another important area of interest is the theory of elliptic functions with applications to nonlinear optics, soliton theory, quantum cryptography, as well as general relativity.
  • 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: Engineering/Physics Applied Mathematics, University of Central Florida

Graduate level courses

Boundary Value Problems (MA 502), Numerical Linear Algebra for Engineers (MA 532), Numerical Methods in Fluids (MA 595)

Courses for Honors

Calculus with Analytic Geometry III (MA 243 H), Differential Equations and Matrix Methods (MA 345H)

Engineering/Physics courses

Tensor Analysis in Engineering Physics, Statics, Mechanics, Vibrational Analysis, Finite Element Methods, Dynamics, Nonlinear Dynamics, Chaotical Systems

4th year courses

Linear Algebra (MA 432), Advanced Engineering Mathematics I (MA 441), Advanced Engineering Mathematics II (MA 442), Complex Analysis (MA 443), Fluid Mechanics (MA 488), Special Topics (Capstone with Lab Research) (MA 499)

3rd year courses

Differential Equations and Matrix Methods (MA 345), Numerical Analysis I (MA 348/MA 438), Special Topics (MA 399)

2nd year courses

Calculus with Analytic Geometry I, II and III (MA 241, MA 242 and MA 243), Business Statistics (MA222)

1st year courses

College Mathematics for Aviation I (MA 111), College Mathematics for Aviation II (MA 112), Analytic Trigonometry (MA 142)

  • Articles  in Refereed Journals (48)

2023 (2)

1. Rosu, S. C. & Mancas, S. C., One-parameter Darboux-deformed Fibonacci numbers. Modern Physics Letters A, 38 (4), 2350022.

2. Mancas, S. C. Rosu, H. C. & Acharya, K. Liouville soliton surfaces obtained using Darboux transformations. Physica Scripta, 98 (7), 075227.

2021 (3)

1. Mancas, S. C, Rosu, H. C., & Hsieh, C-C. Radius evolution for bubbles with elastic shells. (2021). Communications in Nonlinear Science and Numerical Simulation, 103, 106003.

2. Rosu, H. C., Mancas, S. C, & Hsieh, C-C. Superfluid Rayleigh-Plesset extension of FLRW cosmology. (2021). Annals of Physics, 429, 168490.

3. Cornejo-Perez, O., Mancas S. C., Rosu H. C., & Rico-Olvera, C. A. (2021). Inhomogeneous Lienard equation with cubic and quadratic nonlinearity: Solutions obtained through factorization, Revista Mexicana de Fisica, 67(3), 443-446.

2020 (2)

1. Flores-Garduno E., Mancas S. C., Rosu H. C., & P erez-Maldonado M. (2020). Planar motion with Fresnel integrals as components of the velocity. Revista Mexicana de Fisica, 66(5), 585-588.

2. Rousseaux G., & Mancas, S. C. (2020). Visco-elastic Cosmology for a Sparkling Universe?. General Relativity and Gravitation, 52(55), 1-8.

2019 (4)

1. Mancas, S. C. & Adams, R. (2019). Dissipative periodic and chaotic patterns to the KdV-Burgers and Gardner equations. Chaos, Solitons & Fractals, 126, 385{393.

2. Rosu, H. C., Mancas, S. C., & Hsieh, C-C. (2019). Generalized Cornu-type spirals and their Darboux parametric deformations. Physics Letters A, 383, 2692{2697.

3. Mancas, S. C. (2019). Traveling wave solutions to Kawahara and related equations. Differential Equations and Dynamical Systems, 27(1{3), 19-37.

4. Adams, R., Mancas, S. C, & Rosu, H. C. (2019). Stability analysis of orbital modes for a generalized Lane-Emden equation. Communications in Nonlinear Science and Numerical Simulation, 68, 63-71.

2018 (5)

1. Hereman, W. A. & Mancas, S. C. (2018). Traveling Wave Solutions to Fifth- and Seventh order Korteweg-de Vries Equations: Sech and Cn Solutions. Journal of the Physical Society of Japan, 87, 114002.

2. Mancas, S. C., Rosu, H. C. & M. Perez-Maldonado. (2018). Traveling-wave solutions for wave equations with two exponential nonlinearities. Zeitschrift fur Naturforschung A, 73(10), 883-892.

3. Mancas, S. C. & Rosu, H. C. (2018). Two integrable classes of Emden-Fowler equations with applications in astrophysics cosmology. Zeitschrift fur Naturforschung A, 73(9), 805-814.

4. Rosu, H. C., Mancas, S. C., & Flores-Garduno, E. (2018). Riccati parametric deformations of the Cornu spiral. Zeitschrift fur Naturforschung A, 73(6), 479{484.

5. Adams, R. & Mancas, S. C. (2018). Stability of solitary and cnoidal traveling wave solutions for a fifth order Korteweg-de Vries equation. Applied Mathematics and Computation, 321, 745-751.

2017 (2)

1. 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.

2. 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.

2016 (6)

1. 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.

2. Mancas, S. C. & Rosu, H. C. (2016). Evolution of spherical cavitation bubbles: Parametric and closed-form solutions. Physics of Fluids, 28(2), 022009.

3. Reyes, M. A., Gutierrez-Ruiz, D., Mancas, S. C., & Rosu, H. C. (2016). Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations. Modern Physics Letters A, 31(03), 1650020.

4. 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.

5. Rosu H. C. & Mancas, S. C. (2016). Ermakov equation and Camassa-Holm waves. The Nepali Mathematical Sciences Report. 34(1), 47-51.

6. Mancas, S. C., Sajjadi, S. G., Anderson, A., & Ho man, 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.

2015 (7)

1. B erard, F., Vandamme, C. J., & Mancas, S. C. (2015). Two{dimensional structures in the quintic Ginzburg{Landau equation. Nonlinear Dynamics, 81(3), 1413-1433.

2. 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.

3. Mancas, S. C. & Rosu, H. C. (2015). Integrable equations with Ermakov{Pinney nonlinearities and Chiellini damping. Applied Mathematics and Computation, 259, 1-11.

4. Rosu, H. C., Mancas, S. C., & Chen, P. (2015). Barotropic FRW cosmologies with Chiellini damping. Physics Letters A, 379(10), 882-887.

5. Rosu, H. C., Mancas, S. C., & Chen, P. (2015). One{parameter supersymmetric Hamiltonians in momentum space. Physica Scripta, 90(5), 055208.

6. Mancas, S. C. & Choudhury, R. S. (2015). Pulses and snakes in Ginzburg-Landau equation. Nonlinear Dynamics, 79(1), 549-571.

7. Sajjadi, S. G., Mancas, S. C., & Drullion, F. (2015). Formation of three{dimensional surface waves on deep water using elliptic solutions of nonlinear Schrödinger equation. Advances and Applications in Fluid Mechanics, 18(1), 81-112

2014 (4)

1. Uprety, K. N. & Mancas, S. C. (2014). Variable viscosity condition in the modeling of a slider bearing. Neural, Parallel, and Scientific Computations, 22(3), 451-460.

2. Mancas, S. C. & Rosu, H. C. (2014). Ermakov{Lewis invariants and Reid systems. Physics Letters A, 378(30), 2113-2117.

3. 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.

4. 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.

2013 (2)

1. 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.

2. 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).

2011 (1)

1. Mancas, S. C., Khanal, H., & Sajjadi, S. G. (2011). Solitary waves, periodic and elliptic solutions to the Benjamin, Bona & Mahony (BBM) equation modified by viscosity. Advances and Applications in Fluid Mechanics, 9(1), 1-16

2010 (1)

1. Bérard, 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.

2009 (4)

1. 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.

2. 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.

3. 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.

4. 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.

2007 (3)

1. 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.

2. 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.

3. 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.

2006 (2)

1. Mancas, S. C. & Choudhury, S. R. (2006). Traveling wavetrains in the complex cubic-quintic Ginzburg-Landau equation. Chaos, Solitons & Fractals, 28(3), 834-843.

2. Mancas, S. C. & 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), 1256-1271.


  • Publications in Proceedings: (8)

2023 (1)

1. Gonzalez, G. & Rosu, H. C. & Cornejo-Perez, O. & Mancas, S. C., Factorization conditions for nonlinear second-order differential equations. Nonlinear and Modern Mathematical Physics: NMMP-2022. Springer Proceedings in Mathematics & Statistics.

2020 (1)

1. Rosu, H. C., & Mancas, S. C. (2020). Factorization of the Riesz-Feller Fractional Quantum Harmonic Oscillators. Quantum Fest. Journal of Physics: Conference Series, 1540, 01200.

2016 (2)

1. Sajjadi, S. G. & Mancas, S. C. (2016). Formation of wave groups by wind using inhomogeneous nonlinear Schrodinger equation. IMA Conference on Turbulence, Waves and Mixing, in Honor of Lord Julian Hunt's 75th Birthday.

2. Rosu, H. C. & Mancas, S. C. (2016). Ermakov equation and Camassa-Holm waves. IMA Conference on Turbulence, Waves and Mixing, in Honor of Lord Julian Hunt's 75th Birthday.

2012 (1)

1. Vandamme C. J. & Mancas, S. C. (2012). 2D novel structures along an optical  ber. Proceedings of the International Conference on Geometry, Integrability and Quantization, 14, 227-243.

2011 (1)

1. Khanal, H., Mancas, S. C., & Sajjadi, S. G. (2011). Interactions and focusing of nonlinear water waves. Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2011, 26{30 June 2011. II, 703-714, arXiv:1301.4219.

2008 (2)

1. Khanal, H. & Mancas, S. C. (2008). Numerical simulations of five novel classes of dissipative solitons. Proceedings of the 2008 International Conference CMMSE La Manga, Murcia, Spain, 13-17 June 2008, II. 354-364, arXiv:1305.1192.

2. Mancas, S. C. & Choudhury, S. R. (2008). Periodic and chaotic traveling wave patterns in reaction-diffusion/ predator-prey models with general nonlinearities. Proceedings of the 2008 International Conference CMMSE La Manga, Murcia, Spain, 13-17 June 2008. II. 391-412, arXiv:1302.2499.



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