scholarly journals Group Classification and Conservation Laws of a Class of Hyperbolic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
J. C. Ndogmo
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Linear Dependence ◽  
Hyperbolic Equations ◽  
Group Classification ◽  
The Family ◽  
The Given ◽  
Low Order

Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.

scholarly journals Lie group classification of first-order delay ordinary differential equations

2018 ◽  
Vol 51 (20) ◽  
pp. 205202 ◽  
Author(s):  
Vladimir A Dorodnitsyn ◽  
Roman Kozlov ◽  
Sergey V Meleshko ◽  
Pavel Winternitz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Classification ◽  
First Order ◽  
Lie Group Classification

Conservation laws and null divergences

1983 ◽  
Vol 94 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Existence Of Solutions ◽  
Complete Classification ◽  
Complete Analysis ◽  
Partial Differential ◽  
Physical Systems

For a system of partial differential equations, the existence of appropriate conservation laws is often a key ingredient in the investigation of its solutions and their properties. Conservation laws can be used in proving existence of solutions, decay and scattering properties, investigation of singularities, analysis of integrability properties of the system and so on. Representative applications, and more complete bibliographies on conservation laws, can be found in references [7], [8], [12], [19]. The more conservation laws known for a given system, the more tools available for the above investigations. Thus a complete classification of all conservation laws of a given system is of great interest. Not many physical systems have been subjected to such a complete analysis, but two examples can be found in [11] and [14]. The present paper arose from investigations ([15], [16]) into the conservation laws of the equations of elasticity.

scholarly journals Some Connections between Classical and Nonclassical Symmetries of a Partial Differential Equation and Their Applications

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 524
Author(s):  
Chaolu Temuer ◽  
Laga Tong ◽  
George Bluman
Keyword(s):  
Sufficient Conditions ◽  
Partial Differential ◽  
Burgers Equations ◽  
Classical Symmetry ◽  
Nonclassical Symmetry ◽  
Kdv Type Equations ◽  
Nonclassical Symmetries ◽  
The Given

Essential connections between the classical symmetry and nonclassical symmetry of a partial differential equations (PDEs) are established. Through these connections, the sufficient conditions for the nonclassical symmetry of PDEs can be derived directly from the inconsistent conditions of the system determining equations of the classical symmetry of the PDE. Based on the connections, a new algorithm for determining the nonclassical symmetry of a PDEs is proposed. The algorithm make the determination of the nonclassical symmetry easier by adding compatibility extra equations obtained from system of determining equations of the classical symmetry to the system of determining equations of the nonclassical symmetry of the PDE. The findings of this study not only give an alternative method to determine the nonclassical symmetry of a PDE, but also can help for better understanding of the essential connections between classical and nonclassical symmetries of a PDE. Concurrently, the results obtained here enhance the efficiency of the existing algorithms for determining the nonclassical symmetry of a PDE. As applications of the given algorithm, a nonclassical symmetry classification of a class of generalized Burgers equations and the nonclassical symmetries of a KdV-type equations are given within a relatively easier way and some new nonclassical symmetries have been found for the Burgers equations.

scholarly journals SYSTEMATIC ARRANGEMENT OF THE NORTH AMERICAN LEPIDOPTERA

1901 ◽  
Vol 33 (4) ◽  
pp. 116-118
Author(s):  
A. Radcliffe Grote
Keyword(s):  
North American ◽  
Scientific Reason ◽  
The North ◽  
Family Names ◽  
The Family

The first attempt at an arrangement of the N. Am. Lepidoptera, including a reform in the nomenclature, which I published in 1896, calls for some corrections. In the present list I have endeavoured to supply these, but, doubtless, there are others which have escaped me. Since 1896, Lord Walsingham and Mr. Durrant have fixed the types of the genera Tortrix, Tinea, Alucita and Pterophorus, in the two former confirming my doubtful determination of 1895 and correcting the type of the last named genus to monodactyla. I have followed Dyar, in Can. Ent., in using Hipocritidæ instead of Arctiidæ. I cannot find the sure type of Geometra or Noctua. I reject, however, the latter name, since it was differently used by Klein in 1753, and the assumption of 1758 as the basis of nomenclature is arbitrary. The present arrangement is based on that of the Syst. Lep. Hild., 1895. The views of Dyar with regard to the value of the larval tubercles are adopted. The superfamilies are regarded as parallel growths. It seems probable that the Hesperiades, Sphingides, Saturniades and Bombycides (Agrotides) are separate developments from the Tineid phylum. The subfamilies mark breaks in the sequence. This latter is arbitrary, but no scientific reason has been adduced for changing the general Linnæan plan, which is practically the most convenient. With regard to the family names, the oldest term, employed in a collective form and not preoccupied, is retained. At a time when new Catalogues are preparing, the publication of systems will be useful. The diurnals are arranged according to the diphyletic classification of 1897, the sequence and value of the groups are given by me in April, 1900. With regard to the origin of the Lepidoptera, the Micropterygides show hymenopteriform and trichopteriform, the Hepialides neuropteriform characteristics.

scholarly journals Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2083
Author(s):  
María S. Bruzón ◽  
Tamara M. Garrido-Letrán ◽  
Rafael de la Rosa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Soliton Solutions ◽  
Third Order ◽  
Partial Differential ◽  
Symmetry Reductions ◽  
Multipliers Method ◽  
The Family

The Benjamin–Bona–Mahony equation describes the unidirectional propagation of small-amplitude long waves on the surface of water in a channel. In this paper, we consider a family of generalized Benjamin–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function G(u). We study this family from the standpoint of the theory of symmetry reductions of partial differential equations. Firstly, we obtain the Lie point symmetries admitted by the considered family. Moreover, taking into account the admitted point symmetries, we perform symmetry reductions. In particular, for G′(u)≠0, we construct an optimal system of one-dimensional subalgebras for each maximal Lie algebra and deduce the corresponding (1+1)-dimensional nonlinear third-order partial differential equations. Then, we apply Kudryashov’s method to look for exact solutions of the nonlinear differential equation. We also determine line soliton solutions of the family of equations in a particular case. Lastly, through the multipliers method, we have constructed low-order conservation laws admitted by the family of equations.

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