A Partial Differential Equation Arising in a 1D Model for the 3D Vorticity Equation
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We continue the study of the one-dimensional model for the vorticity equation considered in [4]. The partial differential equation σyt+σσxy=σxσy+νσyxx is deduced, which appears as a generalization of the Burgers' equation, with possibly some connection also to the KdV equation. Some properties of this equation are given and propagating solutions are found which are of soliton type, both with non-compact and compact support.Keywords:
Fisher's equation
Universal differential equation
Fisher's equation
Irrational number
sine-Gordon equation
Universal differential equation
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In this paper, the simplest equation method is used to construct exact traveling solutions of the -dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations.
Fisher's equation
Fisher equation
Bernoulli differential equation
Independent equation
Universal differential equation
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We consider the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the hedgehog ansatz is studied. The Bogomol'nyi equation becomes a second-order autonomous nonlinear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.
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This paper studies the equation of a homogeneous type,which is the generalized form of homogenous equation in the first order differential equation.The procedure of solving the homogenous differential equation by a variable transformation method is generalized to solve equations of the homogenous type.Meanwhile,the author proves that the equation of a homogenous type is an integrable equation and gets some new integrable differential equations of the first order,including Reccati equation and Bernoulli equation.
Bernoulli differential equation
Homogeneous differential equation
Universal differential equation
Fisher's equation
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We continue the study of the one-dimensional model for the vorticity equation considered in [4]. The partial differential equation σyt+σσxy=σxσy+νσyxx is deduced, which appears as a generalization of the Burgers' equation, with possibly some connection also to the KdV equation. Some properties of this equation are given and propagating solutions are found which are of soliton type, both with non-compact and compact support.
Fisher's equation
Universal differential equation
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Citations (57)
We successfully constructed wide classes of exact solutions for the Burgers equation by using the generalized simplest equation method. This method yielded a Bäcklund transformation between the Burgers equation and a related constraint equation. By dealing with the constraint equation, we obtained the traveling wave solutions and non-traveling wave solutions of the Burgers equation.
Fisher's equation
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Fisher's equation
Fisher equation
Independent equation
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Abstract Benjamin-Ono Equation are significantly important in describes the one-dimensional internal waves in deep water. Because of its significance, Lie symmetry reduction were chosen to reduce the equation and hence solve the equation. Lie symmetry analysis is one of the powerful methods to solve partial differential equation. Due to its effectiveness, this method is widely applied in solving equation in various field. In this paper, calculation of symmetry of the equation was first present, followed by reduction of the equation. The equation are reduced from non-linear partial differential equation (PDE) to ordinary differential equation (ODE) and hence analytic solution of the partial differential equation was obtained by solving the reduced ODE.
Bernoulli differential equation
Universal differential equation
Fisher's equation
Ode
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We continue the study of the one-dimensional model for the vorticity equation considered in [4]. The partial differential equation σyt+σσxy=σxσy+νσyxx is deduced, which appears as a generalization of the Burgers' equation, with possibly some connection also to the KdV equation. Some properties of this equation are given and propagating solutions are found which are of soliton type, both with non-compact and compact support.
Fisher's equation
Universal differential equation
Cite
Citations (3)