Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (<svg style="vertical-align:-0.252pt;width:45.3125px;" id="M1" height="20.1625" version="1.1" viewBox="0 0 45.3125 20.1625" width="45.3125" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,20.1625)"><g transform="translate(72,-55.87)"><text transform="matrix(1,0,0,-1,-71.95,56.17)"><tspan style="font-size: 17.93px; " x="0" y="0">𝐺</tspan></text><text transform="matrix(1,0,0,-1,-58.43,63.44)"><tspan style="font-size: 12.55px; " x="0" y="0">′</tspan></text><text transform="matrix(1,0,0,-1,-54.3,56.17)"><tspan style="font-size: 17.93px; " x="0" y="0">/</tspan><tspan style="font-size: 17.93px; " x="4.985374" y="0">𝐺</tspan></text></g></g></svg>)-Expansion Method

<table>Solitons solution for <svg height="13.725" id="M152" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 262.0625 13.725" width="262.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.725)">
<g transform="translate(72,-61.02)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.806911" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="38.184162" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="48.636669" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="60.677059" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="66.928558" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="73.180061" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="82.557312" y="0">𝛾</tspan>
<tspan style="font-size: 12.50px; " x="92.372162" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="104.41255" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="110.66405" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="120.04131" y="0">𝜆</tspan>
<tspan style="font-size: 12.50px; " x="130.28127" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="142.32166" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="148.57315" y="0">,</tspan>
</text>
<text transform="matrix(1,0,0,-1,86,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="5.551332" y="0">n</tspan>
<tspan style="font-size: 12.50px; " x="11.802832" y="0">d</tspan>
</text>
<text transform="matrix(1,0,0,-1,108.23,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">2</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (<svg style="vertical-align:-0.252pt;width:45.3125px;" id="M1" height="20.1625" version="1.1" viewBox="0 0 45.3125 20.1625" width="45.3125" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,20.1625)"><g transform="translate(72,-55.87)"><text transform="matrix(1,0,0,-1,-71.95,56.17)"><tspan style="font-size: 17.93px; " x="0" y="0">𝐺</tspan></text><text transform="matrix(1,0,0,-1,-58.43,63.44)"><tspan style="font-size: 12.55px; " x="0" y="0">′</tspan></text><text transform="matrix(1,0,0,-1,-54.3,56.17)"><tspan style="font-size: 17.93px; " x="0" y="0">/</tspan><tspan style="font-size: 17.93px; " x="4.985374" y="0">𝐺</tspan></text></g></g></svg>)-Expansion Method 

Mathematical Problems in Engineering

Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (𝐺′/𝐺)-Expansion Method

Figure 4

Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved ()-Expansion Method