Skip to main content
    • Aa
    • Aa

Euler operators and conservation laws of the BBM equation

  • Peter J. Olver (a1)

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(1) Kh. O. Abdulloev , I. L. Bogolubsky and V. G. Makhankov One more example of inelastic soliton interaction. Phys. Lett. 56 A (1976), 427428.

(2) T. B. Benjamin , J. L. Bona and J. J. Mahony Model equations for long waves in non-linear dispersive systems. Phil. Trans. Roy. Soc. London, Ser. A272 (1972), 4778.

(4) J. C. Eilbeck and G. R. McGuire Numerical study of the regularized long wave equation. I. Numerical methods. J. Computational Phys. 19 (1975), 4357.

(5) J. C. Eilbeck and G. R. McGuire Numerical study of the regularized long wave equation. II. Interaction of solitary waves. J. Computational Phys. 23 (1977), 6373.

(8) D. J. Korteweg and G. De Vries On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. May. 39 (1895), 422443.

(9) M. D. Kruskal , R. M. Miura , C. S. Gardner and N. J. Zabusky Korteweg–de Vries equation and generalizations. V. Uniqueness and nonexistence of polynomial conservation laws. J. Math. Phys. 11 (1970), 952960.

(10) P. D. Lax Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 (1968), 467490.

(11) P. D. Lax Almost periodic solutions of the KdV equation. SIAM Rev. 18 (1976), 351375.

(12) R. M. Miura The Korteweg–de Vries equation: a survey of results. SIAM Rev. 18 (1976), 412458.

(13) R. M. Miura , C. S. Gardner and M. D. Kruskal Korteweg–de Vries equation and generalizations. II. Existence of conservation laws and constants of motion. J. Math. Phys. 9 (1968), 12041209.

(14) P. J. Olver Evolution equations possessing infinitely many symmetries. J. Math. Phys. 18 (1977), 12121215.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 106 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.