Abstract
Based on the fundamental equations of geophysical fluid dynamics and on the consequence of vertical density stratification, travelling wave coordinates are used in this work to study the geometric topological structures of nonlinear permanent wave in phase plane. Rigorous mathematical mechanics demonstrate that the solution of permanent solitary wave does not exist. Hamilton functions and “action-angle” variables are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.
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