K. Porsezian

Bio: K. Porsezian is an academic researcher from Pondicherry University. The author has contributed to research in topics: Soliton & Modulational instability. The author has an hindex of 39, co-authored 283 publications receiving 5487 citations. Previous affiliations of K. Porsezian include Bharathidasan University & Moscow State University.

Generating mechanism for higher-order rogue waves.

Abstract: We introduce a mechanism for generating higher-order rogue waves (HRWs) of the nonlinear Schrodinger (NLS) equation: the progressive fusion and fission of n degenerate breathers associated with a critical eigenvalue λ(0) creates an order-n HRW. By adjusting the relative phase of the breathers in the interacting area, it is possible to obtain different types of HRWs. The value λ(0) is a zero point of an eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order-n HRW.

On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain

Abstract: The integrability aspects of a classical one‐dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter ‘‘a’’ are studied. Through a differential geometric approach, the dynamical equation for the spin chain is expressed in the form of a higher‐order generalized nonlinear Schrodinger equation (GNLSE). An integrable biquadratic chain that is a deformation of the lower‐order continuum isotropic spin chain, is identified by carrying out a Painleve singularity structure analysis on the GNLSE (also through gauge analysis) and its properties are discussed briefly. For the nonintegrable chain, the perturbed soliton solution is obtained through a multiple scale analysis.

Optical solitons in presence of Kerr dispersion and self-frequency shift.

Abstract: We consider the higher order nonlinear Schr\"odinger (HNLS) equation describing nonlinear wave propagation in light guides with all higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. Using the Painlev\'e analysis, we derive all parametric conditions for soliton-type pulse propagation in HNLS fiber system. We generalize the Ablowitz-Kaup-Newell-Segur method to the $3\ifmmode\times\else\texttimes\fi{}3$ eigenvalue problem, and constructed the Lax pair for the integrable case. The one soliton solution is generated from a B\"acklund transformation and an exact N-soliton solution is explicitly obtained from the Hirota bilinearization. The significance of the soliton solution is discussed.

Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation.

Abstract: In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrodinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter γ(1), denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by γ(1) are discussed in detail.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Bose-Einstein condensation in a gas of sodium atoms

Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.