Euler operators and conservation laws of the BBM equation

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.

[1]  Robert M. Miura,et al.  Korteweg‐deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws , 1970 .

[2]  J. Bona,et al.  Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[3]  P. Lax.  INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .

[4]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[5]  T. Jaroszewicz,et al.  Non-eikonal propagation effects in the multiple scattering of hadrons from nuclei at medium energies , 1975 .

[6]  Peter J. Olver,et al.  Evolution equations possessing infinitely many symmetries , 1977 .

[7]  J. C. Eilbeck,et al.  Numerical study of the regularized long-wave equation I: Numerical methods , 1975 .

[8]  I. Gel'fand,et al.  A Lie algebra structure in a formal variational calculation , 1976 .

[9]  L. R. Scott,et al.  Solitary‐wave interaction , 1980 .

[10]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[11]  G. R. McGuire,et al.  Numerical Study of the Regularized Long-Wave Equation. II: Interaction of Solitary Waves , 1977 .

[12]  Peter D. Lax,et al.  Almost Periodic Solutions of the KdV Equation , 1976 .

[13]  C. S. Gardner,et al.  Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion , 1968 .

[14]  V. G. Makhankov,et al.  One more example of inelastic soliton interaction , 1976 .

[15]  A resolution of the euler operator. I , 1978 .

[16]  R. Miura.  The Korteweg–deVries Equation: A Survey of Results , 1976 .