3,671 research outputs found
New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order
In a recent communication Nail Ibragimov introduced the concept of
nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear
self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44,
432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint
classification of a general class of fifth-order evolution equation with time
dependent coefficients is presented. As a result five subclasses of nonlinearly
self-adjoint equations of fifth-order and four subclasses of nonlinearly
self-adjoint equations of third-order are obtained. From the Ibragimov's
theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J.
Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of
these equations are established
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
Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations
The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out
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