Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices

What is it about?

Necessary conditions for breathers to approximate discrete breathers

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Why is it important?

The new results show that the stationary breather solution is a consistent solution of both the quasi-continuum sine-Gordon equation and the forced/damped sine-Gordon system. However, the moving breather is only a consistent solution of the quasi-continuum sine-Gordon equation and not the damped sine-Gordon system.