Partha Guha

Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.

We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).

In this paper we derive the Lie algebraic formulation of the Chen–Lee–Liu (CLL) type generalization of derivative nonlinear Schrödinger equation. We also explore its Lie algebraic connection to another derivative nonlinear Schrödinger equation, the Kaup–Newell system. Finally it is shown that the CLL equation is related to the Dodd–Caudrey–Gibbon equation after averaging over the carrier oscillation.

In this paper we derive the KdV–Burgers and higher order nonlinear Schrodinger equations as an Euler–Poincaré flow on the joint space of Hill's and first order differential operators on circle. We also study a quasi-hamiltonian pair of involution equations one member of which is the KdV–Burger equation.