论文信息 - New conservation laws of some third-order systems of pdes arising from higher-order multipliers

New conservation laws of some third-order systems of pdes arising from higher-order multipliers

Abstract In this paper, we study conservation laws for some third-order systems of pdes, viz., some versions of the Boussinesq equations and the BBM equation. It is shown that new and interesting conserved quantities arise from ‘multipliers’ that are of order greater than one in derivatives of the dependent variables. Furthermore, the invariance properties of the conserved flows with respect to the Lie point symmetry generators are investigated via the symmetry action on the multipliers.

R. Morris | A. H. Kara | A. Kara | R. Morris

[1] M. Karaca,et al. Similarity Reductions of Benjamin-Bona-Mahony Equation , 2008 .

[2] A. Kara,et al. Symmetries, Conservation Laws and Multipliers via Partial Lagrangians and Noether’s Theorem for Classically Non-Variational Problems , 2007 .

[3] Min Chen,et al. Long-time asymptotic behavior of dissipative Boussinesq systems , 2006, math/0607708.

[4] Nikolai A. Kudryashov,et al. Seven common errors in finding exact solutions of nonlinear differential equations , 2009, 1011.4268.

[5] J H Nixon,et al. Application of Lie groups and differentiable manifolds to general methods for simplifying systems of partial differential equations , 1991 .

[6] Fazal M. Mahomed,et al. Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians , 2006 .

[7] Stephen C. Anco,et al. Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications , 2001, European Journal of Applied Mathematics.