Lie symmetries of the shigesada–Kawasaki–Teramoto system
Reads0
Chats0
TLDR
It is proved that the Shigesada–Kawasaki–Teramoto system admits a wide range of different Lie symmetries depending on coefficient values, and the Lie symmetry operators with highly unusual structure are unveiled and applied for finding exact solutions of the relevant nonlinear system with cross-diffusion.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2017-04-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Spacetime symmetries & Adjoint representation.read more
Citations
More filters
Journal ArticleDOI
Generalized exponential rational function method for extended Zakharov–Kuzetsov equation with conformable derivative
TL;DR: In this article, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov-Kuzetsov (FEZK) equation of conformable derivative are investigated.
Journal ArticleDOI
Double-wave solutions and Lie symmetry analysis to the (2 + 1)-dimensional coupled Burgers equations
Mohamed S. Osman,Mohamed S. Osman,Dumitru Baleanu,Abdullahi Rashid Adem,Kamyar Hosseini,Mohammad Mirzazadeh,Mostafa Eslami +6 more
TL;DR: In this paper, a series of double-wave solutions of the (2+1)-dimensional coupled Burgers equations are derived by making use of the generalized unified method (GUM), and the Lie symmetry technique (LST) is also utilized for the symmetry reductions.
Journal ArticleDOI
Local conservation laws, symmetries, and exact solutions for a Kudryashov-Sinelshchikov equation
Journal ArticleDOI
A hunter-gatherer-farmer population model: Lie symmetries, exact solutions and their interpretation
Roman Cherniha,Vasyl' Davydovych +1 more
TL;DR: The Lie symmetry classification of the known three-component reaction-diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived in this article.
Journal ArticleDOI
Symmetry reductions of the ( 3 + 1 ) $(3+1)$ -dimensional modified Zakharov–Kuznetsov equation
TL;DR: In this article, the symmetry reductions of the modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma were studied, where the direct symmetry method was applied to determine the symmetry and the corresponding vector field.
References
More filters
Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Journal ArticleDOI
Spatial Segregation of Interacting Species
TL;DR: It is suggested that the heterogeneity of the environment and the non-linear dispersive movements raise a spatial segregation of the populations of two similar and competing species and there is a possibility that this spatial segregation acts to stabilize the coexistence of twoSimilar species, relaxing the interspecific competition.
Book
Symmetry and Integration Methods for Differential Equations
George W. Bluman,Stephen C. Anco +1 more
TL;DR: In this paper, Lie Groups of Transformations and Infinitesimal Transformations (LGTL) are used for dimensionality analysis, modeling, and invariance in Dimensional Analysis, Modeling and Invariance.
Journal ArticleDOI
Diffusion, Self-Diffusion and Cross-Diffusion
Yuan Lou,Wei Ming Ni +1 more
TL;DR: In this paper, the authors proposed a mathematical model for spatial segregation of interacting species, where u1 and u2 represent the densities of two competing species, d1 and d2 are their diffu- sion rates, a1 and a2 denote the intrinsic growth rates, b1 and c2 account for intra specific competitions, b2 and c1 are the coefficients of inter-specific competitions, :11 and :22 are usually referred as selfdiffusion pressures, and :12 and :21 are cross-diffusion pressure.
BookDOI
Symmetry analysis and exact solutions of equations of nonlinear mathematical physics
TL;DR: In this paper, the authors present a system of PDEs invariant under the Galilei group for nonlinear scalar fields. But they do not consider the nonlinear PDE invariants of the Extended Poincare Algebra AP(1,3).
Related Papers (5)
Symmetry and exact solution of heat-mass transfer equations in thermonuclear plasma
Roman Cherniha,H. Wilhelmsson +1 more