Breather surface

From Wikipedia, the free encyclopedia

This article or section is in need of attention from an expert on the subject.

WikiProject Mathematics or the Mathematics Portal may be able to help recruit one.

If a more appropriate WikiProject or portal exists, please adjust this template accordingly.

Breather surface when $a=\frac{2}{5}\text{ and }-14\le u<14$ $\text{ and }-37.4\le v<37.4$

In differential equations, a breather surface is a mathematical surface relating to breathers.

[edit] Parametrization

$\begin{align} x & {} = \frac{2\left(1-a^2\right)\cosh(au)\sinh(au)}{a\left(\sqrt{1-a^2}\cosh^2(au)+\left(a\,\sin^2\left(\sqrt{1-a^2}v\right)\right)\right)}-u \\ \\ y & {} = \frac{2\sqrt{1-a^2}\cosh(u)\left(-\sqrt{1-a^2}\cos(v)\cos\left(\sqrt{1-a^2}v\right)-\sin(v)\sin\left(\sqrt{1-a^2}v\right)\right)}{a\left(\sqrt{1-a^2}\cosh^2(au)+\left(a\,\sin^2\left(\sqrt{1-a^2}v\right)\right)\right)} \\ \\ z & {} = \frac{2\sqrt{1-a^2}\cosh(au)\left(-\sqrt{1-a^2}\sin(v)\cos\left(\sqrt{1-a^2}v\right)+\cos(v)\sin\left(\sqrt{1-a^2}v\right)\right)}{a\left(\sqrt{1-a^2}\cosh^2(au)+\left(a\,\sin^2\left(\sqrt{1-a^2}v\right)\right)\right)} \end{align}$