Lie symmetry analysis, multiple exp-function method and conservation laws for the (2+1)-dimensional Boussinesq equation
Sivenathi Oscar Mbusi, Abdullahi Rashid Adem, B. Muatjetjeja
Abstract
Abstract In this study, we take into account the (2 + 1)-dimensional Boussinesq equation, a nonlinear evolution partial differential equation that describes how gravity waves move across the surface of the ocean. The symmetry reductions and group invariant precise solutions are systematically determined using the Lie symmetry analysis. We derive the precise multiple wave solutions using the multiple exp-function method, and then, using the multiplier method, we give the conservation laws. The dynamics of complicated waves and their interplay are faithfully recreated by the findings.
Topics & Concepts
Conservation lawPartial differential equationPhysicsInvariant (physics)Symmetry (geometry)Nonlinear systemBoussinesq approximation (buoyancy)Multiplier (economics)Function (biology)Classical mechanicsMathematical analysisMathematical physicsMathematicsMechanicsQuantum mechanicsGeometryConvectionNatural convectionRayleigh numberEvolutionary biologyEconomicsBiologyMacroeconomicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems