Euler operators and conservation laws of the BBM equation
- 1 January 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 85 (1), 143-160
- https://doi.org/10.1017/s0305004100055572
Abstract
The BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.Keywords
This publication has 15 references indexed in Scilit:
- A Resolution of the Euler Operator. IProceedings of the American Mathematical Society, 1978
- A resolution of the Euler operator. IProceedings of the American Mathematical Society, 1978
- Evolution equations possessing infinitely many symmetriesJournal of Mathematical Physics, 1977
- Numerical study of the regularized long-wave equation. II: Interaction of solitary wavesJournal of Computational Physics, 1977
- A Lie algebra structure in a formal variational calculationFunctional Analysis and Its Applications, 1976
- Numerical study of the regularized long-wave equation I: Numerical methodsJournal of Computational Physics, 1975
- Model equations for long waves in nonlinear dispersive systemsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of MotionJournal of Mathematical Physics, 1968
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1895