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Exact Traveling‐Wave Solutions for Model Geophysical Systems
Author(s) -
Sachdev P. L.,
Gupta Neelam
Publication year - 1990
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 - 10.1002/sapm1990824267
Subject(s) - nonlinear system , algebraic number , geophysical fluid dynamics , mathematical analysis , mathematics , rank (graph theory) , geophysics , physics , rossby wave , dynamical systems theory , classical mechanics , mechanics , quantum mechanics , combinatorics , atmospheric sciences
Exact traveling‐wave solutions of time‐dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.