Journal ArticleDOI
Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics
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TLDR
In this article, He's Exp-function method (EFM) was used to construct solitary and soliton solutions of the nonlinear evolution equation, which is a powerful method to overcome some difficulties in nonlinear problems.Abstract:
Purpose – The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.Design/methodology/approach – This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.Findings – This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.Originality/value – The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.read more
Citations
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Journal ArticleDOI
Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(Φ(ξ)/2)-expansion method
TL;DR: In this paper, the Schrodinger type nonlinear evolution equations were analyzed by improved tan(Φ( ξ )/2)-expansion method, which provided a straightforward and powerful mathematical tool for solving problems in nonlinear optic.
Journal ArticleDOI
Interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation for nonlinear waves
TL;DR: In this paper, two types of interaction solutions including lump-kink and lump-soliton ones are derived through mixing two positive quadratic functions with an exponential function, or two Positive Quadratic Functions with a hyperbolic cosine function in the bilinear equation.
Journal ArticleDOI
Abundant soliton solutions for the Kundu–Eckhaus equation via tan(ϕ(ξ))-expansion method
Jalil Manafian,Mehrdad Lakestani +1 more
TL;DR: In this article, the improved tan Φ ( ξ ) / 2 -expansion method is proposed to seek more general exact solutions of the Kundu-Eckhaus equation.
Journal ArticleDOI
Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws
TL;DR: This paper conducts the Painleve analysis of the novel (2+1)-dimensional Kadomtsev-Petviashvili type equations and derives the soliton solutions and gives the formula of the N -soliton solution, which is proved by means of the Hirota condition.
Journal ArticleDOI
Optical solitons with Biswas-Milovic equation for Kerr law nonlinearity
Jalil Manafian,Mehrdad Lakestani +1 more
TL;DR: In this paper, the authors presented the one-soliton solution to the Biswas-Milovic equation with Kerr law nonlinearity, which admits physical significance in applications.
References
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Journal ArticleDOI
Impulses and Physiological States in Theoretical Models of Nerve Membrane
TL;DR: Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve.
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Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
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An Active Pulse Transmission Line Simulating Nerve Axon
TL;DR: In this paper, an active pulse transmission line using tunnel diodes was made to electronically simulate an animal nerve axon, and the equation of propagation for this line is the same as that for a simplified model of nerve membrane treated elsewhere.
Journal ArticleDOI
Variational iteration method – a kind of non-linear analytical technique: some examples
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Book
The direct method in soliton theory
TL;DR: In this paper, Bilinearization of soliton equations is discussed and the Backlund transformation is used to transform the soliton equation into a linear combination of determinants and pfaffians.
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