A recursion formula for the construction of local conservation laws of differential equations

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• 作者：A.F. Cheviakov^a ; ¹ ; ^{shevyakov@math.usask.ca} ; R. Naz^b ; ^{drrehana@lahoreschool.edu.pk}
• 关键词：Local conservation laws ; Partial differential equations ; Ordinary differential equations ; Nonlinear equations of mathematical physics
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：198-212
• 全文大小：432 K
• 卷排序：448

文摘

A simple formula is presented that, for any given local divergence-type conservation law of a system of partial or ordinary differential equations (PDE, ODE), generates a divergence expression involving an arbitrary function of all independent variables. In the cases when the new flux vector is a local expression inequivalent to the initial local conservation law flux vector, a new local conservation law is obtained. For ODEs, this can yield additional integrated factors. Examples of systems of differential equations are presented for which the proposed new relationship yields important local conservation laws starting from basic ones. Examples include a nonlinear ODE and several fundamental physical PDE models, in particular, general classes of nonlinear wave and diffusion equations, vorticity-type equations, and a shear wave propagation model in hyper-viscoelastic fiber-reinforced solids.