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Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and “action-angle” varia-bles 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.
Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification, traveling wave coordinates are used in this work to study the geometric topologicalstructures 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 ” varia-bles are used to express the traveling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.