Trigonometric Function Periodic Wave Solutions and Their Limit Forms for the KdV-Like and the PC-Like Equations

<table>The locations of <svg height="19.762501" id="M480" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 12.375 19.762501" width="12.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.7625)">
<g transform="translate(72,-56.19)">
<text transform="matrix(1,0,0,-1,-71.95,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-67.72,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="-0.25" y="8.1899996">𝜇</tspan>
</text>
</g>
</g>
</svg> and <svg height="19.762501" id="M481" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 12.375 19.762501" width="12.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.7625)">
<g transform="translate(72,-56.19)">
<text transform="matrix(1,0,0,-1,-71.95,60.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan>
</text>
<text transform="matrix(1,0,0,-1,-67.72,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="-0.25" y="8.1899996">𝜇</tspan>
</text>
</g>
</g>
</svg> when <svg height="11.0625" id="M482" style="vertical-align:-0.30096pt" version="1.1" viewbox="0 0 33.8125 11.0625" width="33.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
<tspan style="font-size: 12.50px; " x="8.6520758" y="0">&lt;</tspan>
<tspan style="font-size: 12.50px; " x="20.692465" y="0">0</tspan>
</text>
</g>
</g>
</svg> and <svg height="14.6" id="M483" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 68.925003 14.6" width="68.925003" 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">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="15.641253" y="0">𝑏</tspan>
<tspan style="font-size: 12.50px; " x="21.517662" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="29.156996" y="0">∈</tspan>
<tspan style="font-size: 12.50px; " x="41.197384" y="0">𝐴</tspan>
</text>
<text transform="matrix(1,0,0,-1,-21.78,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig12

Figure 12

Figure 12: Trigonometric Function Periodic Wave Solutions and Their Limit Forms for the KdV-Like and the PC-Like Equations 