Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations
نویسندگان
چکیده
منابع مشابه
Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations
In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = ( κu+ γu ) xx + uuxxxx + μuxxtt + αuxuxxx + βu 2 xx , (1) where α, β, γ, κ and μ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further ...
متن کاملON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *
The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
متن کاملOn a Class of Fourth-order Nonlinear Difference Equations
We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the...
متن کاملNonclassical symmetries of a class of nonlinear partial differential equations and compatibility
Symmetries play an important role in solving partial differential equations. In this paper, the determining equations for a class of nonlinear partial differential equations with arbitrary order are considered. It is shown that the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition...
متن کاملNonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order
In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using thes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 1999
ISSN: 1776-0852
DOI: 10.2991/jnmp.1999.6.1.6