Breather surface - Alchetron, The Free Social Encyclopedia

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

Parameterization

x = − u + 2 ( 1 − a 2 ) cosh ⁡ ( a u ) sinh ⁡ ( a u ) a ( ( 1 − a 2 ) cosh 2 ⁡ ( a u ) + a 2 sin 2 ⁡ ( 1 − a 2 v ) ) y = 2 1 − a 2 cosh ⁡ ( a u ) ( − 1 − a 2 cos ⁡ ( v ) cos ⁡ ( 1 − a 2 v ) − sin ⁡ ( v ) sin ⁡ ( 1 − a 2 v ) ) a ( ( 1 − a 2 ) cosh 2 ⁡ ( a u ) + a 2 sin 2 ⁡ ( 1 − a 2 v ) ) z = 2 1 − a 2 cosh ⁡ ( a u ) ( − 1 − a 2 sin ⁡ ( v ) cos ⁡ ( 1 − a 2 v ) + cos ⁡ ( v ) sin ⁡ ( 1 − a 2 v ) ) a ( ( 1 − a 2 ) cosh 2 ⁡ ( a u ) + a 2 sin 2 ⁡ ( 1 − a 2 v ) )

where 0 < a < 1.

References

Breather surface Wikipedia

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