Conservation Laws of a Gardner Equation with Time-dependent Coefficients

Bruzón, M. S.; Gandarias, M. L.; Rosa, Rafael de la

doi:10.5890/jand.2015.06.006

Cited by 2 publications

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“…The Gardner equation, also known as combined KdV-mKdV equation, is widely used in various areas of physics, such that plasma physics, fluid dynamics, quantum field theory, and it is a useful model for the description of a great variety of wave phenomena in plasma and solid state. The Gardner equation has been recently considered by different authors [6,12,18,20].…”

Section: Introductionmentioning

confidence: 99%

On the classical and nonclassical symmetries of a generalized Gardner equation

Rosa

Bruzón

2016

Applied Mathematics and Nonlinear Sciences

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In this paper, we consider a generalized Gardner equation from the point of view of classical and nonclassical symmetries in partial differential equations. We perform a complete analysis of the symmetry reductions by using the similarity variables and the similarity solutions which allow us to reduce our equation into an ordinary differential equation. Moreover, we prove that the nonclassical method applied to the equation leads to new symmetries, which cannot be obtained by using the Lie classical method. Finally, we calculate exact travelling wave solutions of the equation by using the simplest equation method.

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Section: Introductionmentioning

confidence: 99%

On the classical and nonclassical symmetries of a generalized Gardner equation

Rosa

Bruzón

2016

Applied Mathematics and Nonlinear Sciences

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“…It is well known due to its many applications in mathematics and physics. Among them, it is noted that symmetry groups can be used to obtain exact solutions of partial differential equations, directly [10,17,20] or by obtaining the similarity variables and the similarity solutions [7,12]; or determine conservation laws [2][3][4]16].…”

Section: Classical Symmetries Of Class (6)mentioning

confidence: 99%

Travelling Wave Solutions of a Generalized Variable-Coefficient Gardner Equation

Rosa

Bruzón

2016

SEMA SIMAI Springer Series

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In this paper, a simple way to construct exact solutions by using equivalence transformations is shown. We consider a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We obtain the continuous equivalence transformations of the equation in order to reduce the number of arbitrary functions and give a clearer formulation of the results. Furthermore, we calculate Lie symmetries of the reduced equation. Then, we determine the similarity variables and the similarity solutions which allow us to reduce our equation into an ordinary differential equation. Finally, we obtain some exact travelling wave solutions of the equation by using the simplest equation method.

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Conservation Laws of a Gardner Equation with Time-dependent Coefficients

Cited by 2 publications

References 0 publications

On the classical and nonclassical symmetries of a generalized Gardner equation

On the classical and nonclassical symmetries of a generalized Gardner equation

Travelling Wave Solutions of a Generalized Variable-Coefficient Gardner Equation

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