# solitary wave

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## solitary wave

[′säl·ə‚ter·ē ′wāv]
(physics)
A traveling wave in which a single disturbance is neither preceded by nor followed by other such disturbances, but which does not involve unusually large amplitudes or rapid changes in variables, in contrast to a shock wave.
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Knupp, K., 2006: Observational analysis of a gust front to bore to solitary wave transition within an evolving nocturnal boundary layer.
Thus, in order to investigate the existence of periodic wave solutions and nonexistence of solitary wave solutions of system (1.1), we only need to prove the existence of periodic solutions and nonexistence of homoclinic solutions of system (1.1).
The governing equation of solitary wave amplitude still cannot be obtained from (14), and we continue solving the following high-order problem:
Figures 3 and 4 represent the solitary wave of the real part of [E.sub.2](x, t) in (32) and [N.sub.2](x, t) in (33) for -5 [less than or equal to] x [less than or equal to] 5, 0 [less than or equal to] t [less than or equal to] 1.
Shape of Solitary Waves via Numerical Approximations
Comparisons of internal solitary wave and surface wave actions on marine structures and their responses.
This set of nonlinear equations was derived previously to describe the satellite-measured coherent solitary waves excited in the two-fluid system in space plasmas.
In this section, the numerical algorithm is applied to the following three test problems: the motion of a single solitary wave, the interaction of two solitary waves, and a Maxwellian initial condition.
As a special and important branch of waves, Rossby solitary waves have important theoretical significance and research value.
In soliton theory, nonlinear PDEs associated with some linear spectral problems can be generally classified as the isospectral equations which often describe solitary waves in lossless and uniform media and the nonisospectral equations describing the solitary waves in a certain type of nonuniform media.
With time going on, the moving mesh trajectory is plotted in Figure 1; the feature of the moving process indicates that most of the points focus on nearby solitary waves and move with the propagation of the solitary wave, which also demonstrates the superiority of the moving mesh method.
Since the analysis of the solitary wave shoaling and breaking given here depend on the exact formula for the solitary wave, [[theta].sup.2] = 7/9 is used in the present work.

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