8 research outputs found
Dynamical Studies of Equations from the Gambier Family
We consider the hierarchy of higher-order Riccati equations and establish
their connection with the Gambier equation. Moreover we investigate the
relation of equations of the Gambier family to other nonlinear differential
systems. In particular we explore their connection to the generalized
Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the
consequence of introducing Okamoto's folding transformation which maps the
reduced Gambier equation to a Li\'enard type equation. Finally the conjugate
Hamiltonian aspects of certain equations belonging to this family and their
connection with superintegrability are explored
Singular Lagrangian, Hamiltonization and Jacobi last multiplier for certain biological systems
We study the construction of singular Lagrangians using Jacobi's last multiplier (JLM). We also demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonian of the Host-Parasite model and a Lotka-Volterra mutualistic system, both of which are well known first-order systems of differential equations arising in biology
Quantum integrable systems
This book presents and clarifies the developments of the last ten years in quantum integrable systems. After a preliminary discussion of the fundamentals of classical nonlinear integrable systems, the authors explore the quantum domain. Their approach emphasizes physical systems and the use of concrete examples, and they take care to establish the relationship between new and older methods. The presentation includes the first comprehensive discussion of the quantum Bäcklund transformation Q-operator and various techniques related to algebraic Bethe Ansatz that are not available elsewhere in book form