Kalpana Kalpana (Editor)

Breather surface

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Breather surface

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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