By introducing a Lagrangian transformation such that the space coordinates follow the fluid motion, a range of nonlinear problems in fluid dynamics and plasma theory can be either solved or at least simplified. This can often be done without recourse to an amplitude expansion. Although the idea of using Lagrangian coordinates in hydrodynamics is one of the oldest it theoretical mechanics, most results in plasma physics are of recent date. Somewhat surprisingly, so are some relatively simple examples in fluid dynamics. Similarly, Lagrangian coordinate methods used in a statistical description of a fluid can also be extended to plasma physics.
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