Open AccessGuided solitary waves
Author(s) -
John W. Miles
Publication year - 1980
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.77.4.1723
Subject(s) - dispersion (optics) , physics , parametric statistics , nonlinear system , complex conjugate , mathematical analysis , interval (graph theory) , wave propagation , mechanical wave , dispersion relation , love wave , classical mechanics , gravity wave , mechanics , mathematics , longitudinal wave , optics , quantum mechanics , statistics , combinatorics
Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.