Research Articleshttps://hdl.handle.net/20.500.14155/1992024-03-29T06:59:39Z2024-03-29T06:59:39ZGroup classification, symmetry reductions and exact solutions of a generalized Korteweg-de Vries-Burgers equationMolati, M.Khaliqu, C. M.Adem, A.R.https://hdl.handle.net/20.500.14155/14602023-12-06T09:59:59Z2015-01-01T00:00:00ZGroup classification, symmetry reductions and exact solutions of a generalized Korteweg-de Vries-Burgers equation
Molati, M.; Khaliqu, C. M.; Adem, A.R.
Lie group classification is performed on the generalized Korteweg-de Vries-Burgers equationut+δuxxx+g(u)ux−νuxx+γu=f(x), which occurs in many applications of physical phenomena. We show that the equation admits a four-dimensional equivalenceLie algebra. It is also shown that the principal Lie algebra consists of a single translation symmetry. Several possibleextensions of theprincipal Lie algebra are computed and their associated symmetry reductions and exact solutions are obtained. Also, one-dimensionaloptimal system of subalgebras is obtained for the case when the principal Lie algebra is extended by two symmetries.
2015-01-01T00:00:00ZDirect approach to a group classification problem: Fisher equation with time-dependent coefficientsMolati, M.Khalique, C. M.https://hdl.handle.net/20.500.14155/14592023-12-06T10:00:29Z2016-01-01T00:00:00ZDirect approach to a group classification problem: Fisher equation with time-dependent coefficients
Molati, M.; Khalique, C. M.
We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations.
2016-01-01T00:00:00ZExact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry analysis approachMolati, M.Murakawa, H.https://hdl.handle.net/20.500.14155/14572023-12-06T10:01:03Z2019-01-01T00:00:00ZExact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry analysis approach
Molati, M.; Murakawa, H.
We derive some exact solutions of a nonlinear diffusion-convection-reaction equation which models biological, chemical and physical phenomena. The Lie symmetry classification approach is employed to specify the model parameters and then the symmetries of resulting submodels are utilized for construction of exact solutions.
2019-01-01T00:00:00ZChaos-based Encryption Keys and Neural Key-store for Cloudhosted Data ConfidentialityMosola, N.N.Dlamini, M.T.Blackledge, J.M.Eloff, J.H.P.Venter, H.S.https://hdl.handle.net/20.500.14155/14442023-01-24T13:03:09Z2017-09-01T00:00:00ZChaos-based Encryption Keys and Neural Key-store for Cloudhosted Data Confidentiality
Mosola, N.N.; Dlamini, M.T.; Blackledge, J.M.; Eloff, J.H.P.; Venter, H.S.
Cloud computing brings flexible and cost effective
services. However, security concerns plague the cloud. Data
confidentiality is one of the concerns inhibiting the adoption of
cloud computing. This concern stems from various cyberattacks
directed towards gaining unauthorised access to cloud-bound or
cloud-hosted data. This paper proposes a client-end encryption
and key management system to curb attacks that targets
compromising the confidentiality of cloud-hosted data. The
proposed system uses chaotic atmospheric noise to generate a
fitness function. The fitness function generates random numbers
which create encryption keys. The strength of the encryption keys
is derived from the chaotic and random nature of the atmospheric
noise. The keys are then used for encrypting cloud-bound data
using Advanced Encryption Standard (AES-128, 192 and 256),
Data Encryption Standard (DES), 3-DES, and our novel
cryptosystem named Cryptor, before it can be sent to the cloud.
However, encryption bears no significance if the key management
is flawed. To address the inherent key management problem, the
solution uses a neural network to learn patterns of an encryption
key. Once learnt, the key is then discard to thwart possible key
attacks. The key is reconstructed by the neural network for
decryption purposes.
Southern Africa Telecommunication Networks and Applications Conference (SATNAC) 2017, 3-10 September 2017, Freedom of the Seas Cruise
2017-09-01T00:00:00Z