The Most Unstable Conditions of Modulation Instability

<table>The maximum wave crest histories (a) and scatter diagram (b) of Stokes-modulated wave train for <svg height="14.9375" id="M72" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 60.525002 14.9375" width="60.525002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9375)">
<g transform="translate(72,-60.05)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.55,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">5</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M73" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 51.512501 14.6" width="51.512501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.85,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.5,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.405136" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M74" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 64.074997 10.9125" width="64.074997" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="32.395271" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.646774" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="44.898273" y="0">4</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.3875" id="M75" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.8125 14.3875" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">0</tspan>
</text>
</g>
</g>
</svg>/Δ<i>t</i> =64 with different <i>M. </i></table>

Journal of Applied Mathematics

The Most Unstable Conditions of Modulation Instability

Figure 5