For p=2,3,4, the coefficient beta_1^{(p)}(h) controlling the exponentially small width of the p-th Stokes-wave isolas has explicit deep-water asymptotics, namely (3*sqrt(3)/64)e^{-h/2}, (2*sqrt(2)/3)e^{-2h}, and -(5*sqrt(5)/(8*sqrt(3)))e^{-2h}.
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On higher order isolas of unstable Stokes waves
For p=2,3,4, the coefficient beta_1^{(p)}(h) controlling the exponentially small width of the p-th Stokes-wave isolas has explicit deep-water asymptotics, namely (3*sqrt(3)/64)e^{-h/2}, (2*sqrt(2)/3)e^{-2h}, and -(5*sqrt(5)/(8*sqrt(3)))e^{-2h}.