This study investigates the propagation characteristics of spin waves in an yttrium iron garnet waveguide using a vector network analyzer and a real-time oscilloscope. We confirm the propagation of backward volume magnetostatic spin waves in the linear regime. Solitary spin-wave formation was observed, and the transition from linear to nonlinear response was verified by establishing a threshold power. In the nonlinear regime, collision experiments between two spin waves were conducted, revealing a dependence of attenuation on the input carrier frequency. A comparison with the transmission loss curve confirms the correlation between attenuation and the position of “frequency regions with strong dispersion.” Notably, only within a specific frequency range among these regions do the colliding spin waves maintain their shapes and momenta, passing through each other without dissipation. This remarkable phenomenon is crucial for dissipation-free information transfer. Our findings offer valuable insights into spin-wave behavior, particularly for developing spin-wave-based logic and long-distance magnonic soliton information transfer.