Equivalence group of a fourth-order evolution equation unifying various non-linear models

Gandarias, M. L.; Ibragimov, Nail H.

doi:10.1016/j.cnsns.2005.12.011

Cited by 19 publications

(24 citation statements)

References 11 publications

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“…We were also able to characterize those solutions as solutions for some lower-order ODEs and moreover we obtained some particular solutions. In [10] we found and employed the Lie algebra of the generators of the equivalence transformations for the general model (1).…”

Section: Introductionmentioning

confidence: 99%

Self-adjoint sub-classes of generalized thin film equations

Bruzón

Gandarias

Ibragimov

2009

Journal of Mathematical Analysis and Applications

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In this work we consider a class of fourth-order nonlinear partial differential equation containing several un-specified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without classical Lagrangians.

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Section: Introductionmentioning

confidence: 99%

Self-adjoint sub-classes of generalized thin film equations

Bruzón

Gandarias

Ibragimov

2009

Journal of Mathematical Analysis and Applications

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“…Equivalence transformations play an important role in the study of partial differential equations involving arbitrary functions due to the fact that these allow an exhaustive study and a simple and clear formulation of the results [8,9,14,15,18,19].…”

Section: Introductionmentioning

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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“…This is a group of point transformations that maps members of C to members of C [3,Sect. 6.4], [18][19][20]. The equivalence group can be used for parameter removal after classifying symmetries.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic symmetry classification with invariance

Lisle

Huang

2009

J Eng Math

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Symmetry classification for a system of differential equations can be achieved algorithmically by applying a differential reduction and completion algorithm to the infinitesimal determining equations of the system. The branches of the classification should be invariant under the action of the equivalence group. We show that such invariance can be tested algorithmically knowing only the determining equations of the equivalence group. The method relies on computing the prolongation of a group operator reduced modulo these determining equations. The method is implemented in Maple: a novel pivot selection strategy is able to guide the rifsimp command towards more favourable branchings.

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Equivalence group of a fourth-order evolution equation unifying various non-linear models

Cited by 19 publications

References 11 publications

Self-adjoint sub-classes of generalized thin film equations

Self-adjoint sub-classes of generalized thin film equations

Travelling Wave Solutions of a Generalized Variable-Coefficient Gardner Equation

Algorithmic symmetry classification with invariance

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