Publications on integrable systems

I. Monge-Ampere Equations

Nutku, Y., ``Covariant symplectic structure of the complex Monge-Ampere equation" Physics Letters A 268 (2000) 293

Nutku, Y., ``Hamiltonian structure of real Monge-Ampere equations", J. Phys. A 29 (1996) 3257

Ferapontov, E. V. and Y. Nutku, ``On the Monge-Ampere equivalent of the sine-Gordon equation", J. Phys. A: Math. and Gen. 27 (1994) 7831

Nutku, Y. and O. Sarioglu, ``An integrable family of Monge-Amp\`ere equations and their multi-Hamiltonian structure" Phys. Lett. A 173 (1993) 270

Mokhov, O. I. and Y. Nutku, ``Bianchi transformation between the real hyperbolic Monge-Ampere equation and the Born-Infeld equation" Lett. in Math. Phys. 32 (1994) 121

Galvao, C. A. P. and Y. Nutku, ``Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory" J. Math. Phys. 37 (1996) 6012

Kalayci, J. and Y. Nutku ``Bi-Hamiltonian structure of a WDVV equation in 2-d topological field theory" Phys. Lett. A 227 (1997) 177

Ferapontov, E. V., C. A. P. Galvao, O. I. Mokhov and Y. Nutku, ``Bi-Hamiltonian structure of equations of associativity in 2-d topological field theory" Comm. Math. Phys. 186 (1997) 649

Kalayci, J. and Y. Nutku, ``Alternative bi-Hamiltonian structures for WDVV equations in 2-d topological field theory", J. Phys. A: Math. and Gen. 31 (1998) 723

Nutku, Y., M. B. Sheftel', A. A. Malykh and P. Winternitz ``Invariant Solutions to Complex Monge-Ampere Equation and Gravitational Instantons" Yadernaya Fisica 61 (1998) 1874
 
 

II Hamiltonian structure

Nutku Y. ``New symplectic structure for KdV" To be published in "Integrable Hierarchies and Modern Physics Theories, NATO ARW-UIC 2000" Editors H. Aratyn and A. Sorin.

Nutku, Y., ``Canonical formulation of shallow water waves" J. Phys. A: Math. and Gen. 16 (1983) 4195

Nutku, Y., ``Hamiltonian formulation of the KdV equation" J. Math. Phys. 26 (1984) 2007

Neyzi, F. and Y. Nutku, ``Canonical structures for dispersive waves in shallow water" J. Math. Phys. 28 (1987) 1499

Nutku, Y. and O. Oguz, ``Bi-Hamiltonian structure of coupled KdV equations" Nuovo Cimento 105 B (1990) 1381
 

III Equations of hydrodynamic type

Nutku, Y., ``On a new class of completely integrable nonlinear wave equations, I: Infinitely many conserved quantities" J. Math. Phys. 26 (1985) 1237

Nutku, Y., ``On a new class of completely integrable nonlinear wave equations, II: Multi-Hamiltonian structure" J. Math. Phys. 28 (1987) 2579

Olver, P. J. and Y. Nutku, ``Hamiltonian structures for systems of hyperbolic conservation laws" J. Math. Phys. 29 (1988) 1610

Arik, M., F. Neyzi, Y. Nutku, P. J. Olver and J. M. Verosky, ``Multi-Hamiltonian structure of the Born-Infeld equation" J. Math. Phys. 30 (1989) 1338

Gumral, H. and Y. Nutku, ``Multi-Hamiltonian structure of equations of hydrodynamic type " J. Math. Phys. 31 (1990) 2606

Gumral, H. and Y. Nutku, ``Bi-Hamiltonian structures of d-Boussinesq and Benney-Lax equations", J. Phys. A: Math. and Gen. 27 (1994) 193
 
 

IV Dynamical Systems

Nutku, Y. ``Hamiltonian structure of the Lotka-Volterra equations" Phys. Lett A 145 (1990) 27

Nutku, Y., ``Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics" J. Phys. A: Math. and Gen., 23 (1990) L1145

Gumral, H. and Y. Nutku, ``Poisson structure of dynamical systems with three degrees of freedom", J. Math. Phys. 34 (1993) 5691
 
 

V Miscellaneous

Gurses, M. and Y. Nutku, ``New nonlinear evolution equations from surface theory" J. Math. Phys. 22 (1981) 1393