Associate Professor of Mathematics

Ph.D. (McGill, 1987)

__Office:__ 4279 Herzberg Physics

__Telephone:__ (613) 520-2600 ext. 2126

__e-mail:__ melkonia@math.carleton.ca

Nonlinear differential equations

*A Method of Solution of a Class of Second-Order Ordinary Differential Equations*, International Journal of Applied Mathematical Sciences 17(1) (2024), 1-8, https://www.ripublication.com/jams21/jamsv17n1_1.pdf

*Symmetry groups and integrating factors of total differential equations in three variables*, Far East Journal of Applied Mathematics 116(4) (2023), 377-391. https://dx.doi.org/10.17654/0972096023018

*The General Solution of* du/dx=x-u^{2}, Journal of Research in Applied Mathematics 9(6) (2023), 26-29. https://www.questjournals.org/jram/papers/v9-i6/09062629.pdf

*A Complete Asymptotic Analysis of an Oscillation Free Nonlinear Equation of Bessel Type with a Pole in the Dependent Variable*, Nonlinear Oscillations **13**, No. 2 (2010) 206-239 (with A.B. Mingarelli and J.M. Pacheco-Castelao)

*Two-Dimensional Wavelet Bases for Partial Differential Operators and Applications*, Operator Theory: Advances and Applications **155** (2004) 219-233 (with M.A. Hajji and R. Vaillancourt)

*Representation of Differential Operators in Wavelet Basis*, Computers & Mathematics With Applications **47** (2004) 1011-1033 (with M.A. Hajji and R. Vaillancourt)

*Psi-series solutions of the Henon-Heiles system and their convergence*,
Journal of Nonlinear Mathematical Physics **6**, No. 2 (1999) 139-160

*Convergence of psi-series solutions of the Duffing equation and the Lorenz system*, Nonlinearity **8** (1995) 1143-1157 (with A. Zypchen)

*Convergence of psi-series solutions of nonlinear ordinary differential equations*, Canadian Applied Mathematics Quarterly **3** (1995) 43-88 (with M.A. Hemmi)

*Exact solutions of nonlinear thin-film amplitude evolution equations via transformations*, Canadian Applied Mathematics Quarterly **1** (1993) 493-528

*Symmetry properties and solutions of nonlinear dispersive thin-film equations in three dimensions*, Journal of Mathematical Physics **32** (1991) 3213-3222 (with P. Winternitz)

*Analysis of a nonlinear diffusive amplitude equation for waves
on thin films*, Studies in Applied Mathematics **82** (1990) 37-48 (with S.A. Maslowe)

*Two-dimensional amplitude evolution equations for nonlinear
dispersive waves on thin films*, Physica D **34** (1989) 255-269 (with S.A. Maslowe)

*Nonlinear waves on thin films*, in Continuum Mechanics and Its Applications, eds. G.A.C. Graham and S.K. Malik, Hemisphere Publishing Corporation, New York (1989) 411-423

*A model equation illustrating subcritical instability to long waves in shear flows*, Studies in Applied Mathematics **76** (1987) 265-275 (with I.H. Herron and S.A. Maslowe)

*The propagation of finite-amplitude waves in a model boundary layer*, Studies in Applied Mathematics **76** (1987) 169-185 (with P.M. Balagondar and S.A. Maslowe)