New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

<table>Periodic solution for <svg height="13.55" id="M33" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.480394" y="0">2</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.55" id="M34" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 35.075001 13.55" width="35.075001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
<tspan style="font-size: 12.50px; " x="9.6648188" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.705208" y="0">0</tspan>
</text>
</g>
</g>
</svg> and <svg height="10.9125" id="M35" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.125 10.9125" width="35.125" 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">𝑧</tspan>
<tspan style="font-size: 12.50px; " x="9.7023277" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.742718" y="0">0</tspan>
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</g>
</svg>.</table>

Journal of Applied Mathematics

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Figure 2

Figure 2: New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method 