Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations

Gandarias, M. L.; Khalique, Chaudry Masood

doi:10.1016/j.cnsns.2015.07.010

Cited by 35 publications

(16 citation statements)

References 15 publications

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“…Lie theory is one of the most important and powerful methods used to study differential equations. It has numerous applications in mathematics and physics, among them, to obtain exact solutions, directly or by obtaining similarity variables and similarity solutions (Gandarias and Bruzón, 2012;Gandarias and Khalique, 2016;Pocheketa, Popovych and Vaneeva, 2014); to classify invariant equations; to reduce the number of independent variables or to determine conservation laws (de la Rosa, Gandarias, and Bruzón, 2015;Ibragimov et al, 2015). The problem lies in the fact that the analysis of Lie symmetries of nonlinear equations involving arbitrary functions seems rather difficult.…”

Section: Introductionmentioning

confidence: 98%

Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

Rosa

Gandarias

Bruzón

2016

Journal of Computational and Theoretical Transport

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Symmetry group analysis is carried out on a generalized fifthorder KdV (foKdV) equation involving many arbitrary functions. Equivalence transformations group has been determined. This allows us to perform a comprehensive study by reducing the equation to a subclass with fewer number of arbitrary elements. Furthermore, we have established the subclasses of the reduced equation which are nonlinearly self-adjoint. The property of nonlinearly self-adjointness is used to construct conserved vectors from the classical symmetries of the equation by using a general theorem on conservation laws. We also determine conservation laws by using the multipliers method.

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Section: Introductionmentioning

confidence: 98%

Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

Rosa

Gandarias

Bruzón

2016

Journal of Computational and Theoretical Transport

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“…Many recent papers using this method are in the literature. [25][26][27] The aim of this paper is to consider the following generalization of Equations 1 and 2:…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation

Rosa¹,

Camacho²,

Bruzón³

et al. 2018

Math Methods in App Sciences

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Nonlinear partial differential equations are used to describe complex phenomena in various fields of science. In this work, we consider a generalized fourth‐order nonlinear wave equation from the point of view of the theory of symmetry reductions in partial differential equations. We derive classical symmetries, and we obtain the reductions from the optimal system of subalgebras. We derive all the low‐order conservation laws, and we search for multipliers of the reduced ordinary differential equations that are invariant under a symmetry group to reduce directly the order of the equations.

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“…In [2][3][4][5], Anco and Bluman gave a general algorithmic method to find all conservations laws for evolution equations Many recent papers using this method have been published in [1,11,12]. After Ibragimov's results several papers appeared concerned with self-adjointness and its applications to PDEs [22,23].…”

Section: Introductionmentioning

confidence: 99%

Conservation laws for a strongly damped wave equation

Gandarias

Rosa

2017

Open Physics

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Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations

Cited by 35 publications

References 15 publications

Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation

Conservation laws for a strongly damped wave equation

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