14 research outputs found
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
Symmetry analysis of the bidimensional Lane-Emden systems
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established. (C) 2011 Elsevier Inc. All rights reserved.We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established388212791284FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)SEM INFORMAÇÃOSEM INFORMAÇÃ
Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory
We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors
Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions
A method for symbolically computing conservation laws of nonlinear partial
differential equations (PDEs) in multiple space dimensions is presented in the
language of variational calculus and linear algebra. The steps of the method
are illustrated using the Zakharov-Kuznetsov and Kadomtsev-Petviashvili
equations as examples. The method is algorithmic and has been implemented in
Mathematica. The software package, ConservationLawsMD.m, can be used to
symbolically compute and test conservation laws for polynomial PDEs that can be
written as nonlinear evolution equations. The code ConservationLawsMD.m has
been applied to (2+1)-dimensional versions of the Sawada-Kotera, Camassa-Holm,
and Gardner equations, and the multi-dimensional Khokhlov-Zabolotskaya
equation.Comment: 26 pages. Paper will appear in Journal of Symbolic Computation
(2011). Presented at the Special Session on Geometric Flows, Moving Frames
and Integrable Systems, 2010 Spring Central Sectional Meeting of the American
Mathematical Society, Macalester College, St. Paul, Minnesota, April 10, 201
Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions
In this work, we consider the chiral nonlinear Schrödinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries. 
Conservation Laws of Some Physical Models via Symbolic Package GeM
We study the conservation laws of evolution equation, lubrication models, sinh-Poisson equation, Kaup-Kupershmidt equation, and modified Sawada-Kotera equation. The symbolic software GeM (Cheviakov (2007) and (2010)) is used to derive the multipliers and conservation law fluxes. Software GeM is Maple-based package, and it computes conservation laws by direct method and first homotopy and second homotopy formulas
Conservation Laws and Exact Solutions for a Reaction-Diffusion Equation with a Variable Coefficient
In this paper a variable-coefficient reaction-diffusion equation is studied. We classify the equation into three kinds by different restraints imposed on the variable coefficient b(x) in the process of solving the determining equations of Lie groups. Then, for each kind, the conservation laws corresponding to the symmetries obtained are considered. Finally, some exact solutions are constructed