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Hamiltonian Equations for Scale‐Invariant Waves
Author(s) -
Alì G.,
Hunter J. K.,
Parker D. F.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01416
Subject(s) - inviscid flow , burgers' equation , nonlinear system , mathematics , invariant (physics) , mathematical analysis , scale invariance , magnetohydrodynamics , classical mechanics , hamiltonian (control theory) , hamiltonian formalism , formalism (music) , physics , mathematical physics , partial differential equation , magnetic field , quantum mechanics , mathematical optimization , art , musical , statistics , covariant transformation , visual arts
We use a Hamiltonian formalism to derive equations for weakly nonlinear scale‐invariant waves. We apply the results to nonlinear surface waves in elasticity and magnetohydrodynamics that satisfy nonlocal generalizations of the inviscid Burgers' equation.