Roman O. Popovych

activity

20032005

most citedHierarchy of Conservation Laws of Diffusion--Convection Equations

59 citations · 84 across the 3 of their papers we have counts for

collaborators

3 papers

math-ph2005★ 20 cited

Conservation Laws of Variable Coefficient Diffusion-Convection Equations

N. M. Ivanova, R. O. Popovych, C. Sophocleous

We study local conservation laws of variable coefficient diffusion-convection equations of the form $f (x) u_{t} = (g (x) A (u) u_{x})_{x} + h (x) B (u) u_{x}$ . The main tool of our investigation is the…

math-ph2004★ 59 cited

Hierarchy of Conservation Laws of Diffusion--Convection Equations

Roman O. Popovych, Nataliya M. Ivanova

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or s…

math-ph2003★ 5 cited

Lie Symmetries of (1+1)-Dimensional Cubic Schrödinger Equation with Potential

Roman O. Popovych, Nataliya M. Ivanova, Homayoon Eshraghi

We perform the complete group classification in the class of cubic Schrödinger equations of the form $i ψ_{t} + ψ_{xx} + ψ^{2} ψ^{*} + V (t, x) ψ = 0$ where $V$ is an arbitrary complex-valued potenti…