New PDF release: A blow-up result for the periodic Camassa-Holm equation

By Wahlen E.

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While the model is unlikely to be a perfect fit to the observed phenomena, it represents the changing values well enough to allow you to estimate some answers to questions. If the high tide and low tide are recorded 12 hours apart, a full cycle, from low tide to high 2π π = . Low tide is tide and back to low tide, will take a period of 24 hours. 5. 5  12  The remaining parameter is the phase shift. 5  12  If t = 0 corresponds to some other point in the cycle, you’ll need more information to determine the shift.

The function f (t ) = sin  t  = sin completes only half a wave in the 2  2 space of 2π, taking 4π to complete a full cycle. 5 –2 Y(x)=sin(x) Y(x)=sin(2x) Y(x)=sin(x/2) The final element to consider is the sign of the amplitude and the sign of the frequency. While both the amplitude and the frequency are taken as absolute values, the presence of a negative sign on either one indicates a reflection. A negative value of a indicates that the graph is reflected over the x-axis, and a negative value of b means a reflection over the y-axis.

Y = 4 − 3 cos  2θ −   3 Graphs of other trigonometric functions The sine and cosine graphs are continuous and periodic. They are smooth, connected curves that repeat the wavelike pattern over and over. In different equations, the length, or period, of the wave may change, its height, or amplitude, may change, and it may shift in different directions, but the basic wave form remains the same for all sine and cosine graphs. All the other trigonometric functions have graphs that are discontinuous, but, like the sine and cosine, each repeats a pattern.

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A blow-up result for the periodic Camassa-Holm equation by Wahlen E.

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