arXiv subjects

F M Mahomed

Publications and source records attributed to F M Mahomed.

2 recordsLinked to original sources

arXiv2025

General Classification, Invariance and Conservation Laws Analyses of Nonlinear Fourth Order Wave and Nerve Membrane Equations with Dissipation

We study the nonlinear wave equation for arbitrary function with fourth order dissipation. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth order dissipation. The equivalence transformations, Lie symmetries and a complete classification is presented. We also discuss the one dimensional optimal system in each case obtained via classification. The reduction of the partial differential equations (PDEs) is carried out and the forms of invariant solutions are presented. The study also include the construction of conservation laws using the direct method. The invariant solutions and some special type of solutions including solitions are presented with their graphical illustrations.

nlin.SI↗

arXiv2011

Higher Dimensional Systems of Differential Equations Obtained by Iterative Use of Complex Methods

Systems of two ordinary and partial differential equations (ODEs and PDEs) had been obtained from a scalar complex ODE by splitting it into its real and imaginary parts. The procedure was also carried out to obtain a four dimensional system by splitting a complex system of two ODEs into its real and imaginary parts. Systems of three ODEs had not been accessible by these methods. In this paper the complex splitting is used iteratively to obtain three and four dimensional systems of ODEs and four dimensional systems of PDEs for four functions of two and four variables. The new systems of four ODEs are distinct from the class obtained by the single split of a two dimensional system. Illustrative examples are provided.

math.CA↗