一类新的三阶和五阶非线性自伴发展方程
New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order
摘要：
在最近的一次通信中，Nail Algimov介绍了非线性自伴微分方程的概念[N]。H.李晓云，非线性自伴性与守恒律，物理学报，第一卷，第44卷，43 - 2002年，8页，（2011）]。本文对一类含时系数的五阶发展方程进行了非线性自伴分类。由此得到五阶非线性自伴方程的五个子类和三阶非线性自伴方程的四个子类。本文从守恒律定理出发，H.李志忠，一个新的守恒定理，数学学报.应用程序、Vol.333，311 - 328，（2007）]建立了这些方程中的一些方程的守恒定律。
英文摘要：
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.
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