On Hamiltonian formulations of the C1(m,a,b) equations

Alon Zilburg, Philip Rosenau

Research output: Contribution to journalArticlepeer-review

Abstract

In this letter we re-address a class of genuinely nonlinear third order dispersive equations; C1(m,a,b): ut+(um)x+1/b[ua(ub)xx]x=0, which among other solitary structures admit compactons, and demonstrate that certain subclasses of these equations may be cast into Hamiltonian and Lagrangian formulations resulting in new conservation laws, some of which are nonlocal. In particular, the new nonlocal conservation law of the K(n,n) equations enables us to prove that the response to a certain class of excitations cannot contain only compactons.

Original languageEnglish
Pages (from-to)1557-1562
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume381
Issue number18
DOIs
StatePublished - 10 May 2017

Keywords

  • Compactons
  • Conservation laws
  • Hamiltonians
  • Nonlinear dispersive PDE

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