Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-mathematical-modeling-approach-from-nonlinear-dynamics-to-complex-UTQrk1EU7H
References (36)
-
M. Bruzón, M. Gandarias, R. Rosa (2014)
Conservation Laws of a Family of Reaction-Diffusion-Convection Equations, 7
-
P. Olver (1986)
Applications of lie groups to differential equationsActa Applicandae Mathematica, 20
-
M. Gandarias (2014)
Nonlinear self-adjointness through differential substitutionsCommun. Nonlinear Sci. Numer. Simul., 19
-
R. FitzHugh (1961)
Impulses and Physiological States in Theoretical Models of Nerve Membrane.Biophysical journal, 1 6
-
A. Bokhari, Radwan Al-Rubaee, F. Zaman (2011)
On a generalized Fisher equationCommunications in Nonlinear Science and Numerical Simulation, 16
-
J. Nagumo, Suguru Arimoto, S. Yoshizawa (1962)
An Active Pulse Transmission Line Simulating Nerve AxonProceedings of the IRE, 50
-
M. Rosa, M. Bruzón, M. Gandarias (2015)
Symmetry analysis and exact solutions for a generalized Fisher equation in cylindrical coordinatesCommun. Nonlinear Sci. Numer. Simul., 25
-
A. Bokhari, M. Mustafa, F. Zaman (2008)
An exact solution of a quasilinear Fisher equation in cylindrical coordinatesNonlinear Analysis-theory Methods & Applications, 69
-
M. Rosa, M. Gandarias (2016)
Multiplier method and exact solutions for a density dependent reaction-diffusion equationApplied Mathematics and Nonlinear Sciences, 1
-
M. Gandarias (2011)
Weak self-adjoint differential equationsJournal of Physics A: Mathematical and Theoretical, 44
-
J. Meinhardt (1981)
Symmetries and differential equationsJournal of Physics A, 14
-
R. Moitsheki, O. Makinde (2010)
Classical Lie point symmetry analysis of nonlinear diffusion equations describing thermal energy storageAppl. Math. Comput., 216
-
R. Tracinà, Igor Freire, M. Torrisi (2016)
Nonlinear self-adjointness of a class of third order nonlinear dispersive equationsCommun. Nonlinear Sci. Numer. Simul., 32
-
N. Vitanov (2011)
Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEsCommunications in Nonlinear Science and Numerical Simulation, 16
-
Khadijo Adem, C. Khalique (2015)
Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW EquationMathematical Problems in Engineering, 2015
-
G. Bluman, S. Kumei (1990)
Symmetry-based algorithms to relate partial differential equations: I. Local symmetriesEuropean Journal of Applied Mathematics, 1
-
M. Gandarias, M. Rosa (2016)
On double reductions from symmetries and conservation laws for a damped Boussinesq equationChaos Solitons & Fractals, 89
-
N. Kudryashov (2004)
Simplest equation method to look for exact solutions of nonlinear differential equationsChaos Solitons & Fractals, 24
-
N. Ibragimov (2006)
The answer to the question put to me by L.V. Ovsyannikov 33 years ago, 3
-
G. Bluman, G. Reid, S. Kumei (1988)
New classes of symmetries for partial differential equationsJournal of Mathematical Physics, 29
-
N. Ibragimov (2011)
Nonlinear self-adjointness and conservation lawsJournal of Physics A: Mathematical and Theoretical, 44
-
G. Bluman, J. Cole (1974)
Similarity methods for differential equations -
R. Rosa, M. Gandarias, M. Bruzón (2016)
Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equationCommun. Nonlinear Sci. Numer. Simul., 40
-
S. Anco, G. Bluman (2001)
Direct construction method for conservation laws of partial differential equations Part II: General treatmentEuropean Journal of Applied Mathematics, 13
-
Hans Weinberger, Mark Lewis, Bingtuan Li (2002)
Analysis of linear determinacy for spread in cooperative modelsJournal of Mathematical Biology, 45
-
M. Durán, J. Camacho, M. Bruzón, M. Gandarias (2017)
Classical and potential symmetries for a generalized Fisher equationJ. Comput. Appl. Math., 318
-
M. Rosa, M. Bruzón, M. Gandarias (2015)
A conservation law for a generalized chemical Fisher equationJournal of Mathematical Chemistry, 53
-
I. Krasil’shchik, Alexandre Vinogradov (1989)
Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformationsActa Applicandae Mathematica, 15
-
A. González-López (1988)
Symmetry and integrability by quadratures of ordinary differential equationsPhysics Letters A, 133
-
J. Zeldowitsch, D. Frank-Kamenetzki (1988)
A Theory of Thermal Propagation of Flame -
M. Gandarias, M. Bruzón, M. Rosa (2013)
Nonlinear self-adjointness and conservation laws for a generalized Fisher equationCommun. Nonlinear Sci. Numer. Simul., 18
-
R. Cherniha, M. Serov (1998)
Symmetries, ansätze and exact solutions of nonlinear second-order evolution equations with convection terms, IIEuropean Journal of Applied Mathematics, 17
-
R. Fisher (1937)
THE WAVE OF ADVANCE OF ADVANTAGEOUS GENESAnnals of Human Genetics, 7
-
M. Gandarias, C. Khalique (2016)
Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equationsCommun. Nonlinear Sci. Numer. Simul., 32
-
R. Tracinà, M. Bruzón, M. Gandarias (2016)
On the nonlinear self-adjointness of a class of fourth-order evolution equationsAppl. Math. Comput., 275
-
M. Gandarias, M. Bruzón, M. Rosa (2015)
Symmetries and Conservation Laws for Some Compacton EquationMathematical Problems in Engineering, 2015
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG, part of Springer Nature 2019
- ISBN
- 978-3-319-78511-0
- Pages
- 27 –50
- DOI
- 10.1007/978-3-319-78512-7_3
- Publisher site
- See Chapter on Publisher Site
Abstract
[This chapter presents a generalized Fisher equation (GFE) from the point of view of the theory of symmetry reductions in partial differential equations. The GFE can be used to describe an ideal growth and spatial-diffusion phenomena. The reductions to ordinary differential equations are derived from the optimal system of subalgebras and new exact solutions are obtained. Conservation laws for this equation are constructed. The potential system has been achieved from the complete list of the conservation laws. Potential symmetries, which are not local symmetries, are carried out for the generalized Fisher equation, these symmetries lead to the linearization of the equation by non-invertible mappings.]
Published: Jun 15, 2018