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The present research is centered on analyzing and modeling the scattering characteristics of a trifurcated waveguide that includes impedance discontinuities. A mode-matching method, grounded in projecting the solution onto orthogonal basis functions, is devised for the investigation. The impedance disparities at the interfaces are represented in normal velocity modes, which, when combined with pressure modes, result in a linear algebraic system. This system is subsequently truncated and inverted for numerical experimentation. The convergence of scattering amplitudes is assured by reconstructing matching conditions and adhering to conservation laws. The computational results indicate that optimizing attenuation behavior is achievable through manipulating variation bounding properties and impedance discontinuities.

In the present paper, we construct the analytical solutions of some nonlinear equations involving Jumarie's modified Riemann-Liouville derivative in mathematical physics; namely the space–time fractional Calogero-Degasperis (CD) equation and the space–time fractional potential Kadomtsev-Petviashvili (PKP) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. This method is more powerful and will be used in further works to establish more entirely new solutions for other kind of nonlinear fractional PDEs arising in mathematical physics.

The present article highlights the acoustic waves scattering in a trifurcated waveguide containing compressible fluid together with step discontinuities and change of bounding material properties. The study is important because of its applications in active noise control measures, especially used to control the low-frequency noise and related vibrations. The governing boundary value problem is solved by using the mode-matching technique. The solution is developed for the analysis of symmetric, uniform, and non-uniform cross-sections. The solution procedure begins by determining the expanded form of field potentials in various duct regions of the waveguide. Then, the pressures and the normal velocity modes across the waveguide regions are matched at interface. The energy flux against frequency and various duct configurations is plotted. The solution is validated altogether through the apposite analytical and numerical results.