Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term

Rosa, María; Bruzón, María de los Santos; Gandarias, M. L.

doi:10.3934/dcdss.2015.8.1331

Cited by 12 publications

(9 citation statements)

References 17 publications

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“…Rosa et al (2015) applied Lie classical method and -expansion method to Fisher equation and derived some new traveling wave solutions. If setting , then Eq.…”

Section: Resultsmentioning

confidence: 99%

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Traveling wave solutions of the time-delayed generalized Burgers-type equations

et al. 2016

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BackgroundRecently, nonlinear time-delayed evolution equations have received considerable interest due to their numerous applications in the areas of physics, biology, chemistry and so on.MethodsIn this paper, we obtain traveling wave solutions by using the extended -expansion method.ResultsBased on the method, we get many solutions of the time-delayed generalized Burgers-type equations.ConclusionsThe results reveal that the extended -expansion method is direct, effective and can be used for many other nonlinear time-delayed evolution equations.

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“…Rosa et al (2015) applied Lie classical method and -expansion method to Fisher equation and derived some new traveling wave solutions. If setting , then Eq.…”

Section: Resultsmentioning

confidence: 99%

“…(4) becomes Eq. (14) in Rosa and Gandarias, (2015). So if we applied Lie classical method and extended -expansion method to Fisher equation, then many more exact solutions can be obtained.…”

Section: Resultsmentioning

confidence: 99%

Traveling wave solutions of the time-delayed generalized Burgers-type equations

et al. 2016

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“…This method() has been successfully applied for obtaining exact travelling wave solutions of numerous nonlinear PDEs. () In this paper, we apply the method of simplest equation for obtaining exact analytical solutions of the KS Equation .…”

Section: Introductionmentioning

confidence: 99%

“…This method 38,39 has been successfully applied for obtaining exact travelling wave solutions of numerous nonlinear PDEs. [40][41][42] In this paper, we apply the method of simplest equation for obtaining exact analytical solutions of the KS Equation 2.The structure of this paper is as follows: In Section 2, by using the general method of multipliers, 18,19,43 we obtain a complete classification of low-order conservation laws for the KS Equation 2. In Section 3, we derive the Lie symmetries of the KS Equation 2 and its Lie algebras.…”

mentioning

confidence: 99%

Local conservation laws, symmetries, and exact solutions for a Kudryashov‐Sinelshchikov equation

Bruzón

Recio

Rosa

et al. 2017

Math Methods in App Sciences

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In this paper, we consider a Kudryashov‐Sinelshchikov equation that describes pressure waves in a mixture of a liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer between liquid and gas bubbles. We show that this equation is rich in conservation laws. These conservation laws have been found by using the direct method of the multipliers. We apply the Lie group method to derive the symmetries of this equation. Then, by using the optimal system of 1‐dimensional subalgebras we reduce the equation to ordinary differential equations. Finally, some exact wave solutions are obtained by applying the simplest equation method.

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“…The effort in finding exact solutions of nonlinear equations is crucial for understanding most nonlinear physical phenomena. There are several papers in which exact solutions of PDEs are obtained from the similarity reductions [1,4,7,26]. The great utility of similarity solutions is that they may be calculated by solving an ordinary differential equation (ODE) instead of a PDE.…”

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confidence: 99%

Differential invariants of a generalized variable-coefficient Gardner equation

Rosa¹,

Bruzón²

2018

Discrete &Amp; Continuous Dynamical Systems - S

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In this paper, we consider a generalized variable-coefficient Gardner equation. By using the equivalence group of this equation, we derive the differential invariants of first order and the corresponding invariant equations. We employ these differential invariants and invariant equations to find the most general subclass of variable-coefficient Gardner equations which can be mapped into a specific constant-coefficient equation by means of an equivalence transformation. Furthermore, differential invariants are applied to obtain exact solutions.

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Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term

Cited by 12 publications

References 17 publications

Traveling wave solutions of the time-delayed generalized Burgers-type equations

Traveling wave solutions of the time-delayed generalized Burgers-type equations

Local conservation laws, symmetries, and exact solutions for a Kudryashov‐Sinelshchikov equation

Differential invariants of a generalized variable-coefficient Gardner equation

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