Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256321 | Physica D: Nonlinear Phenomena | 2016 | 10 Pages |
Abstract
Whitham modulation theory with degeneracy in wave action is considered. The case where all components of the wave action conservation law, when evaluated on a family of periodic travelling waves, have vanishing derivative with respect to wavenumber is considered. It is shown that Whitham modulation equations morph, on a slower time scale, into the two way Boussinesq equation. Both the 1+1 and 2+1 cases are considered. The resulting Boussinesq equation arises in a universal form, in that the coefficients are determined from the abstract properties of the Lagrangian and do not depend on particular equations. One curious by-product of the analysis is that the theory can be used to confirm that the two-way Boussinesq equation is not a valid model in shallow water hydrodynamics. Modulation of nonlinear travelling waves of the complex Klein-Gordon equation is used to illustrate the theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Daniel J. Ratliff, Thomas J. Bridges,