Exact Solutions and Conservation Laws of A (2+1)-dimensional Combined Potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili Equation
Motshidisi Charity Sebogodi, B. Muatjetjeja, Abdullahi Rashid Adem
Abstract
Abstract This article investigates a sixth order integrable nonlinear partial differential equation model that fulfills the Hirota N-soliton. Space and time-dependent shift, rotation and space-dependent shift, time and space translations, and time and space dilations Lie point symmetries are presented methodically. Under a specific point symmetries, the Lie point symmetries lead to group invariant solutions. The significance of conservation laws of the underlying equation are shown. The results are quite accurate in recreating complex waves and the dynamics of their interactions.
Topics & Concepts
Homogeneous spaceConservation lawKadomtsev–Petviashvili equationIntegrable systemMathematicsInvariant (physics)Partial differential equationSolitonMathematical analysisMathematical physicsSpace (punctuation)Nonlinear systemLie groupBurgers' equationPure mathematicsPhysicsQuantum mechanicsGeometryPhilosophyLinguisticsNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models