Abstract
We show that evolutionary Hirota type Euler-Lagrange equations in (2 + 1) dimensions have a symplectic Monge-Ampre form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two seven-parameter families of integrable equations converted to two-component form we have constructed Lagrangians, recursion operators and bi-Hamiltonian representations. We have also presented a six-parameter family of tri-Hamiltonian systems.
Keywords
Lax pair
Mathematics
Hamiltonian (control theory)
Mathematical physics
Recursion (computer science)
Type (biology)
Pure mathematics
Algebra over a field
Integrable system
Algorithm
Mathematical optimization
Subject Areas
Nonlinear Waves and Solitons
·Statistical and Nonlinear Physics ·Physical Sciences
Nonlinear Photonic Systems
·Statistical and Nonlinear Physics ·Physical Sciences
Advanced Mathematical Physics Problems
·Mathematical Physics ·Physical Sciences
Citations by Year
2018: 1
2019: 2
2022: 2
2023: 1
2024: 1
Loading…
Loading…