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Scaling by Grigory Isaakovich Barenblatt

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Chapter 6Self-similar phenomena and travelling waves

6.1 Travelling waves

In various problems in applied mathematics an important role is played by travelling waves. These are phenomena for which distributions of the properties of motion at different times can be obtained from one another by a translation, rather than by a similarity transformation as in the case of self-similar phenomena. In other words, one can always choose a moving Cartesian coordinate system such that the distribution of properties of a phenomenon of travelling-wave type is stationary in that system.

        In accordance with the definition given above, solutions of travelling-wave type can be expressed in the form

Here v (generally speaking, a vector) is the property ...

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