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.
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.