Solitary wave

solitary wave

A gravity wave consisting of a single elevation of finite amplitude that propagates without change of form.

First described in 1844 by Scott Russell in a British Association Report, its existence is a result of a balance between nonlinearity, which tends to steepen the wave front in consequence of the increase of wave speed with amplitude, and dispersion, which tends to spread the wave front as the wave speed of any spectral component decreases with increasing wavenumber. Most extensively studied are solitary waves on the free surface of a homogeneous, nonrotating fluid of finite depth. Surface solitary waves are also the easiest to observe. However, there also exist internal solitary waves, as the balance between nonlinearity and dispersion may be possible in the absence of a free surface by virtue of any or all of stratification, shear, compressibility, and rotation.
See also envelope soliton.

Miles, J. W. 1980. Solitary waves. Annu. Rev. Fluid Mech.. 12. 11–43.

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Often the greatest magnitude at a given point of any spatially and temporally varying physical quantity governed by a wave equation; can also mean the spatial part of a time-harmonic wave function.