Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via <svg style="vertical-align:-3.186pt;width:59.799999px;" id="M1" height="23.825001" version="1.1" viewBox="0 0 59.799999 23.825001" width="59.799999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,23.825)">
		<g transform="translate(72,-52.94)">
			<text transform="matrix(1,0,0,-1,-71.95,56.17)">
				<tspan style="font-size: 17.93px; " x="0" y="0">(</tspan>
				<tspan style="font-size: 17.93px; " x="5.9716892" y="0">𝐺</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-52.46,63.44)">
				<tspan style="font-size: 12.55px; " x="0" y="0">′</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-48.33,56.17)">
				<tspan style="font-size: 17.93px; " x="0" y="0">/</tspan>
				<tspan style="font-size: 17.93px; " x="4.985374" y="0">𝐺</tspan>
				<tspan style="font-size: 17.93px; " x="18.148195" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>-Expansion Method

<table>Hyperbolic function solution (<a href="https://static.hindawi.com/articles/mpe/volume-2011/424801/figures/#EEq3.9">3.9</a>) of Hirota-Ramani equation, for <svg height="10.85" id="M105" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 35.174999 10.85" width="35.174999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.85)">
<g transform="translate(72,-63.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.8625" id="M106" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 35.799999 10.8625" width="35.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8625)">
<g transform="translate(72,-63.31)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="10.239957" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.280346" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M107" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 50.125 10.9125" width="50.125" 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">𝜔</tspan>
<tspan style="font-size: 12.50px; " x="11.977874" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.018263" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="30.269764" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="33.745598" y="0">2</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.6" id="M108" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 43.912498 14.6" width="43.912498" 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">𝐶</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.56,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-55.21,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
</text>
</g>
</g>
</svg>, and <svg height="14.6" id="M109" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 43.912498 14.6" width="43.912498" 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">𝐶</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.56,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,-55.21,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via <svg style="vertical-align:-3.186pt;width:59.799999px;" id="M1" height="23.825001" version="1.1" viewBox="0 0 59.799999 23.825001" width="59.799999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,23.825)">
		<g transform="translate(72,-52.94)">
			<text transform="matrix(1,0,0,-1,-71.95,56.17)">
				<tspan style="font-size: 17.93px; " x="0" y="0">(</tspan>
				<tspan style="font-size: 17.93px; " x="5.9716892" y="0">𝐺</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-52.46,63.44)">
				<tspan style="font-size: 12.55px; " x="0" y="0">′</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-48.33,56.17)">
				<tspan style="font-size: 17.93px; " x="0" y="0">/</tspan>
				<tspan style="font-size: 17.93px; " x="4.985374" y="0">𝐺</tspan>
				<tspan style="font-size: 17.93px; " x="18.148195" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>-Expansion Method 

Figure 1 | Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via 
	
		
			
				(
				𝐺
			

			
				′
			

			
				/
				𝐺
				)
			

		
	
-Expansion Method 

Mathematical Problems in Engineering

Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via ( 𝐺 ′ / 𝐺 ) -Expansion Method

Figure 1

Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via -Expansion Method