Partha Guha

JD Block, Sector III, Kolkata — 700098, India
Satyendranath Nath Bose National Centre for Basic Sciences


Esen O., Choudhury A. G., Guha P., Gümral H.
Superintegrable Cases of Four-dimensional Dynamical Systems
2016, vol. 21, no. 2, pp.  175-188
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.
Keywords: first integrals, Darboux polynomials, Jacobi’s last multiplier, 4D Poisson structures, tri-Hamiltonian structures, Shivamoggi equations, generalized Raychaudhuri equations, Lü system and Qi system
Citation: Esen O., Choudhury A. G., Guha P., Gümral H.,  Superintegrable Cases of Four-dimensional Dynamical Systems, Regular and Chaotic Dynamics, 2016, vol. 21, no. 2, pp. 175-188
Grammaticos B., Ramani A., Guha P.
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).
Keywords: Painlevé equations, contiguity relations, second-degree differential equations, Hamiltonian formalism
Citation: Grammaticos B., Ramani A., Guha P.,  Second-degree Painlevé Equations and Their Contiguity Relations, Regular and Chaotic Dynamics, 2014, vol. 19, no. 1, pp. 37-47
Guha P.
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.
Citation: Guha P.,  Geometry of Chen–Lee–Liu type derivative nonlinear Schrödinger flow, Regular and Chaotic Dynamics, 2003, vol. 8, no. 2, pp. 213-224
Guha P.
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.
Citation: Guha P.,  Euler–Poincaré Formalism of KDV–Burgers and Higher Order Nonlinear Schrodinger Equations, Regular and Chaotic Dynamics, 2002, vol. 7, no. 4, pp. 425-434

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