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="M81" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 178.2625 14.9375" width="178.2625" 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>
<tspan style="font-size: 12.50px; " x="33.908134" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="43.285385" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-9.15,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-0.81,63.35)">
<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">1</tspan>
<tspan style="font-size: 12.50px; " x="27.656635" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="37.033886" y="0">𝑀</tspan>
<tspan style="font-size: 12.50px; " x="53.075233" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="65.115623" y="0">4</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M82" 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> with different Δ<i>t. </i></table>

Journal of Applied Mathematics

The Most Unstable Conditions of Modulation Instability

Figure 7