Lie point symmetries and conservation laws in microstretch and micromorphic elasticity

2006 ◽  
Vol 44 (20) ◽  
pp. 1571-1582 ◽  
Author(s):  
Markus Lazar ◽  
Charalampos Anastassiadis
Keyword(s):  
Conservation Laws ◽  
Lie Point Symmetries ◽  
Micromorphic Elasticity

scholarly journals On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 65
Author(s):  
Winter Sinkala
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Conservation Law ◽  
The Other ◽  
Multiplier Method ◽  
Lie Point Symmetries ◽  
Mathematical Study ◽  
Black Scholes

Construction of conservation laws of differential equations is an essential part of the mathematical study of differential equations. In this paper we derive, using two approaches, general formulas for finding conservation laws of the Black-Scholes equation. In one approach, we exploit nonlinear self-adjointness and Lie point symmetries of the equation, while in the other approach we use the multiplier method. We present illustrative examples and also show how every solution of the Black-Scholes equation leads to a conservation law of the same equation.

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Partner Ndlovu ◽  
Rasselo Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Conservation Laws ◽  
Linear Function ◽  
Power Law ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Lie Point Symmetries ◽  
Transient Heat Conduction Problem

AbstractSome new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

scholarly journals Symmetries, Conservation Laws, and Wave Equation on the Milne Metric

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmad M. Ahmad ◽  
Ashfaque H. Bokhari ◽  
F. D. Zaman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Conservation Laws ◽  
Mathematical Physics ◽  
Lie Point Symmetries ◽  
Noether Symmetries ◽  
Physical Systems ◽  
Action Integral ◽  
Lorentzian Metric

Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.

scholarly journals Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 341 ◽  
Author(s):  
Aliyu Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Conservation Laws ◽  
Travelling Wave ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Sixth Order ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Analysis Technique ◽  
Conservation Theorem

In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.

scholarly journals On New Conservation Laws of Fin Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Gülden Gün Polat ◽  
Özlem Orhan ◽  
Teoman Özer
Keyword(s):  
Conservation Laws ◽  
Linear Form ◽  
Mathematical Physics ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Multiplier Method ◽  
Lie Point Symmetries ◽  
Invariant Solutions ◽  
Relationship Of ◽  
The Relationship

We study the new conservation forms of the nonlinear fin equation in mathematical physics. In this study, first, Lie point symmetries of the fin equation are identified and classified. Then by using the relationship of Lie symmetry andλ-symmetry, newλ-functions are investigated. In addition, the Jacobi Last Multiplier method and the approach, which is based on the factλ-functions are assumed to be of linear form, are considered as different procedures for lambda symmetry analysis. Finally, the corresponding new conservation laws and invariant solutions of the equation are presented.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Sait San ◽  
Emrullah Yaşar
Keyword(s):  
Liquid Crystals ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Nematic Liquid Crystals ◽  
Lie Point Symmetries ◽  
Local Conservation ◽  
The Relationship ◽  
Conservation Method

We study the modified Hunter-Saxton equation which arises in modelling of nematic liquid crystals. We obtain local conservation laws using the nonlocal conservation method and multiplier approach. In addition, using the relationship between conservation laws and Lie-point symmetries, some reductions and exact solutions are obtained.

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