Abstract
In this work, we show that the integrable (3+1)-dimensional Hirota type nonlinear differential equation reduces to the (2+1)-dimensional Hirota type equation by symmetry reduction. It is proved that starting from the Dirac constraint analysis and degenerate Lagrangian, obtained (2+1)-dimensional equation is also integrable and admit bi-Hamiltonian structure. Moreover, all the parameters defined in four dimensional system like Lagrangian, Hamiltonian operators, Hamiltonian functions and recursion operator have the same result of the three dimensional system after the reduction.
Keywords
Integrable system
Hamiltonian (control theory)
Degenerate energy levels
Mathematical physics
Mathematics
Hamiltonian system
Differential equation
Mathematical analysis
Reduction (mathematics)
Physics
Quantum mechanics
Geometry
Mathematical optimization
Subject Areas
Nonlinear Waves and Solitons
·Statistical and Nonlinear Physics ·Physical Sciences
Nonlinear Photonic Systems
·Statistical and Nonlinear Physics ·Physical Sciences
Algebraic structures and combinatorial models
·Geometry and Topology ·Physical Sciences
Loading…