File:KdV cnoidal parameters 2.svg

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Summary

Parameter relations for <a href="https://en.wikipedia.org/wiki/Cnoidal_wave" class="extiw" title="en:Cnoidal wave">cnoidal wave</a> solutions of the <a href="https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation" class="extiw" title="en:Korteweg–de Vries equation">Korteweg–de Vries equation</a>. Shown is −log₁₀ (1−m), with m the elliptic parameter of the <a href="https://en.wikipedia.org/wiki/Elliptic_integral" class="extiw" title="en:Elliptic integral">complete elliptic integrals</a>, as a function of dimensionless <a href="https://en.wikipedia.org/wiki/Period_(physics)" class="extiw" title="en:Period (physics)">period</a> τ √(g/h) and relative <a href="https://en.wikipedia.org/wiki/Wave_height" class="extiw" title="en:Wave height">wave height</a> H / h. The values along the contour lines are −log₁₀ (1−m), so a value 1 corresponds with m = 1 − 10⁻¹ = 0.9 and a value 40 with m = 1 − 10⁻⁴⁰.

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	19:12, 6 January 2017		635 × 505 (407 KB)	127.0.0.1 (talk)	Parameter relations for <a href="https://en.wikipedia.org/wiki/Cnoidal_wave" class="extiw" title="en:Cnoidal wave">cnoidal wave</a> solutions of the <a href="https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation" class="extiw" title="en:Korteweg–de Vries equation">Korteweg–de Vries equation</a>. Shown is −log<sub>10</sub> (1−<i>m</i>), with <i>m</i> the elliptic parameter of the <a href="https://en.wikipedia.org/wiki/Elliptic_integral" class="extiw" title="en:Elliptic integral">complete elliptic integrals</a>, as a function of dimensionless <a href="https://en.wikipedia.org/wiki/Period_(physics)" class="extiw" title="en:Period (physics)">period</a> <i>τ</i> √(<i>g</i>/<i>h</i>) and relative <a href="https://en.wikipedia.org/wiki/Wave_height" class="extiw" title="en:Wave height">wave height</a> <i>H</i> / <i>h</i>. The values along the contour lines are −log<sub>10</sub> (1−<i>m</i>), so a value 1 corresponds with <i>m</i> = 1 − 10<sup>−1</sup> = 0.9 and a value 40 with <i>m</i> = 1 − 10<sup>−40</sup>.

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