Siraj Ahmad

On the quasi-periodic solutions to the discrete nonlinear Schrodinger equation

The authors have obtained the quasi-periodic solutions to the discrete non-linear Schrodinger equation by a variant of a method due to Date and Tanaka (1976). It is shown explicitly that the non-linear field variables at the different lattice points can be determined in a recursive fashion in terms of combinations of Riemanns theta functions depending on lattice position and time.

The quasiperiodic solutions to the discrete nonlinear Schrödinger equation

The quasiperiodic solutions to the discrete nonlinear Schrodinger equation are obtained by a variant of a method due to Date and Tanaka [E. Date and S. Tanaka, Suppl. Prog. Theor. Phys. 59, 107 (1976)]. It is shown explicitly that the nonlinear field variable at the different lattice points can be determined in a recursive fashion in terms of combinations of Reimann’s functions depending on lattice position and time.

On the prolongation approach in three dimensions for the conservation laws and Lax pair of the Benjamin–Ono equation

The prolongation structure approach of Wahlquist and Estabrook [J. Math. Phys. 16, 1 (1975)] is used effectively in a new situation in relation to the integrodifferential type BO equation (the Benjamin–Ono equation). The main clue lies in the possible differential equation representation of such equations in three dimensions. Here it is shown how the usual analysis of prolongation structure can be utilized to deduce a Lax pair for a BO type equation in three dimensions. Effectiveness of the present approach is further demonstrated by an independent derivation of some conservation laws associated with the equation. Last, the whole formalism is reduced to two dimensions to make contact with known results.

A variational approach to bäcklund and infinitesimal bäcklund transformation for Kadomtsev-Petviashvili equation

Abstract A new form of the Backlund transformation for the Kadomtsev-Petviashvili equation is obtained through the variational formalism. At no stage we use the equation of motion for the deduction of the Backlund transformation. So we follow the method of Steudel for the derivation of the infinite number of conservation laws using Noethers theorem in three dimensions and the corresponding infinitesimal Backlund transformation.