The article explores the modified unstable nonlinear Schrödinger equation (MUNLSE), which models specific instabilities in modulated wave-trains and describes the time evolution of disturbances in marginally stable or unstable media. The authors use three symbolic computational techniques—positive quadratic function approach, three-wave approach, and double exponential approach—to derive novel exact solutions, including rational solitons, multi-wave solutions, and other types of wave solutions. These solutions are obtained through symbolic computation and the ansatz function method, incorporating traveling wave and logarithmic transformations. The derived wave solutions are significant for understanding the physical phenomena of the complex model. The stability of the MUNLSE is evaluated through a comprehensive modulational instability analysis, confirming the stability and exactness of all soliton solutions. The authors also generate 3D visual representations of various wave solutions, such as breather-type waves, lump waves, and multi-peak solitons, and observe intriguing phenomena arising from the interactions among these multi-waves. The findings have applications in a wide range of scientific and engineering disciplines.The article explores the modified unstable nonlinear Schrödinger equation (MUNLSE), which models specific instabilities in modulated wave-trains and describes the time evolution of disturbances in marginally stable or unstable media. The authors use three symbolic computational techniques—positive quadratic function approach, three-wave approach, and double exponential approach—to derive novel exact solutions, including rational solitons, multi-wave solutions, and other types of wave solutions. These solutions are obtained through symbolic computation and the ansatz function method, incorporating traveling wave and logarithmic transformations. The derived wave solutions are significant for understanding the physical phenomena of the complex model. The stability of the MUNLSE is evaluated through a comprehensive modulational instability analysis, confirming the stability and exactness of all soliton solutions. The authors also generate 3D visual representations of various wave solutions, such as breather-type waves, lump waves, and multi-peak solitons, and observe intriguing phenomena arising from the interactions among these multi-waves. The findings have applications in a wide range of scientific and engineering disciplines.