Related papers: Group analysis for generalized reaction-diffusion …
We discuss an application of group theoretical methods to the formulation of the thermodynamics of systems constrained by the conservation laws described by a semi--simple compact Lie group. A general projection method that allows to…
We present several families of nonlinear reaction diffusion equations with variable coefficients including Fisher-KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by…
This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
Using the asymmetric fractional calculus of variations, we derive a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.
In this paper, the relationships between Lie symmetry groups and fundamental solutions for a class of conformable time fractional partial differential equations (PDEs) with variable coefficients are investigated. Specifically, the…
This paper investigates a system of nonlinear reaction-diffusion equations modeling the industrial synthesis of ammonia. By applying Lie group analysis, we construct self-similar solutions and derive a reduced system of ordinary…
A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…
The GENERIC theory provides a framework for the description of non-equilibrium phenomena in isolated systems beyond local thermal equilibrium and beyond linear non-equilibrium (i.e., linear relations between thermodynamic forces and…
In this paper, the problem of approximate symmetries of a class of non-linear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we…
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the…
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…
We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
We perform enhanced Lie symmetry analysis of generalized fifth-order Korteweg-de Vries equations with time-dependent coefficients. The corresponding similarity reductions are classified and some exact solutions are constructed.
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…