109 citations · 291 across the 9 of their papers we have counts for
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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 . The main tool of our investigation is the…
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…
Potential equivalence transformations for nonlinear diffusion-convection equations
Roman O. Popovych, Nataliya M. Ivanova
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are cl…
Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
Roman O. Popovych, Nataliya M. Ivanova, Homayoon Eshraghi
We perform the complete group classification in the class of nonlinear Schrödinger equations of the form where is an arbitrary complex-valued pot…
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 where is an arbitrary complex-valued potenti…
New results on group classification of nonlinear diffusion-convection equations
Roman O. Popovych, Nataliya M. Ivanova
Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient -dimensional no…