The generalized (3+1)-dimensional Breaking soliton system (gBSS) has numerous applications across various scientific fields. This manuscript presents a study on important exact solutions of the gBSS, with a focus on novel solutions. Using the Hirota bilinear technique, we derive the general solution of the proposed system and obtain the novel solutions by considering different types of auxiliary functions. Our analysis includes the study of multi-solitons, multiple bifurcation solitons, lump wave solutions, M-shaped solitons, and their interactions. We also observe several hybrid solitons, including tuning fork-shaped, X-Y shaped, and double Y shaped. Our results are presented through graphical representations.

Double diffusive natural convection (DDNC) is one of the most studied phenomena in convective energy transfer, having applications in heat exchangers, oceanography and climate Science, biological Systems, renewable energy, and geothermal energy systems. We aimed to conduct a numerical analysis of DDNC within a quadrantal enclosure that contained a Cu-Al₂O₃ hybrid nanofluid with water as a host fluid. The motivation for choosing this model was attributed to the relatively limited research conducted within this particular geometric configuration, specifically in the context of double-diffusive natural convection, which served as the primary mode of heat and mass transfer. Using numerical simulations, we focused on the impacts of an external magnetic field. The bottom wall of the quadrantal cavity was kept at high temperatures ${(T}_h)$ and concentrations ${(c}_h),$while the vertical wall maintained at low temperatures ${(T}_c)$and concentrations ${(c}_c)$. Moreover, the curved wall is kept thermally insulated. With an eminent numerical method, the finite element method is employed to solve the governing partial differential equations (PDEs), which are transformed into a dimensionless form. The outcomes were acquainted with streamlines, isoconcentration contours, and isotherms, along with local and average Nusselt and Sherwood numbers. The analysis revealed that enhancing the volume fraction of Cu-Al₂O₃ nanoparticles within the conventional fluid increased heat transfer efficiency by up to 11% compared to the base fluid. It was also noticed that without a magnetic field (Ha = 0), the stream functional measures at its highest value of ${(\psi }_{max}=6.2)$ indicated strong convection. However, with the presence of a magnetic field (Ha = 40), the stream function significantly decreased to ${(\psi }_{max}=0.2)$.