Approximate Damped Oscillatory Solutions for Generalized KdV-Burgers Equation and Their Error Estimates

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<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
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</svg> is an even integer, <svg height="11.0625" id="M460" style="vertical-align:-0.30096pt" version="1.1" viewbox="0 0 34.674999 11.0625" width="34.674999" 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">𝑏</tspan>
<tspan style="font-size: 12.50px; " x="9.3397408" y="0">&gt;</tspan>
<tspan style="font-size: 12.50px; " x="21.380131" y="0">0</tspan>
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<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">&gt;</tspan>
<tspan style="font-size: 12.50px; " x="20.692465" y="0">0</tspan>
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</svg>, <svg height="20.4125" id="M462" style="vertical-align:-5.17902pt" version="1.1" viewbox="0 0 92.762497 20.4125" width="92.762497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.4125)">
<g transform="translate(72,-55.67)">
<text transform="matrix(1,0,0,-1,-71.95,60.88)">
<tspan style="font-size: 12.50px; " x="50.580002" y="1.92">√</tspan>
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">&lt;</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="32.282745" y="0">&lt;</tspan>
<tspan style="font-size: 12.50px; " x="44.323135" y="0">2</tspan>
</text>
<g>
<path d="m -9.77,70.71 11.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-9.77,60.88)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
<tspan style="font-size: 12.50px; " x="6.1139669" y="0">𝑐</tspan>
</text>
</g>
</g>
</svg>).</table>

Abstract and Applied Analysis

fig13

Figure 13

Figure 13: Approximate Damped Oscillatory Solutions for Generalized KdV-Burgers Equation and Their Error Estimates 