<p>This work examines the unstable nonlinear Schrödinger equation, which characterizes the temporal evolution of disturbances in marginally stable or unstable media. The <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\frac{G'}{G},\frac{1}{G})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>,</mo> <mfrac> <mn>1</mn> <mi>G</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-expansion method is employed to derive new exact soliton solutions, explicitly represented through exponential, trigonometric, and rational functions. These exact solutions are then compared with results obtained from the Levenberg–Marquardt artificial neural network and the split-step Fourier numerical method. Statistical analyses, presented through tables and graphs, show strong agreement between the exact solutions and those obtained using these methods. Furthermore, 2-D, contour, and 3-D plots are utilized to visually represent and validate the behavior of the solutions. The results demonstrate that the combination of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\frac{G'}{G},\frac{1}{G})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>,</mo> <mfrac> <mn>1</mn> <mi>G</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-expansion method, the Levenberg–Marquardt artificial neural network, and the split-step Fourier numerical method provides a robust and complementary framework for solving and analyzing the unstable nonlinear Schrödinger equation, offering reliable insights into its dynamic behavior.</p>