Title :
Nonlinear self-adjointness and conservation laws for some third order equations
Author :
Gandarias, M.L. ; Bruzon, M.S.
Author_Institution :
Dept. of Math., Univ. of Cadiz, Cadiz, Spain
Abstract :
The concepts of self-adjoint and quasi-self-adjoint equations were introduced by N.H. Ibragimov, he also proved a general theorem on conservation laws. In 2011 the first of these authors has introduced the definition of weak self-adjoint equations and N.H. Ibragimov has introduced the concept of nonlinear self-adjointness. In this paper we consider a generalized Korteweg-de Vries and the third order potential Burgers equation. By using the property of self-adjointness and it generalizations we construct some conservation laws associated with symmetries of the differential equation.
Keywords :
Korteweg-de Vries equation; conservation laws; partial differential equations; conservation laws; differential equation; general theorem; generalized Korteweg-de Vries; nonlinear self-adjointness; quasiself-adjoint equations; third order potential Burgers equation; weak self-adjoint equations; Complexity theory; Conferences; Equations; Generators; Mathematical model; Partial differential equations; Conservation laws; Nonlinear self-adjointness; Partial differential equations; Symmetries; Weak adjointness;
Conference_Titel :
Nonlinear Science and Complexity (NSC), 2012 IEEE 4th International Conference on
Conference_Location :
Budapest
Print_ISBN :
978-1-4673-2702-2
Electronic_ISBN :
978-1-4673-2701-5
DOI :
10.1109/NSC.2012.6304752
