Soliton solutions, Liouville integrability and gauge equivalence of Sasa Satsuma equation

Exact integrability of the Sasa Satsuma eqation (SSE) in the Liouville sense is established by showing the existence of an infinite set of conservation laws. The explicit form of the conserved quantities in term of the fields are obtained by solving the Riccati equation for the associated 3x3 Lax operator. The soliton solutions in particular, one and two soliton solutions, are constructed by the Hirota's bilinear method. The one soliton solutions is also compared with that found through the inverse scattering method. The gauge equivalence of the SSE with a generalized Landau Lifshitz equation is established with the explicit construction oComment: 14 pages, to be published in J. Math. Phys. April-May, 199

An Adaptive Modulation Scheme for Two-user Fading MAC with Quantized Fade State Feedback

With no CSI at the users, transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the input, is not efficient because error rates will be high when the channel conditions are poor. However, perfect CSI at the users is an unrealistic assumption in the wireless scenario, as it would involve massive feedback overheads. In this paper we propose a scheme which uses only quantized knowledge of CSI at the transmitters with the overhead being nominal. The users rotate their constellation without varying their transmit power to adapt to the existing channel conditions, in order to meet certain pre-determined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal modulation scheme has been described for the case when both the users use symmetric M-PSK constellations at the input, where $M=2^\lambda$, $\lambda$ being a positive integer. The strategy has been illustrated by considering examples where both users use QPSK or 8-PSK signal sets at the input. It is shown that the proposed scheme has better throughput and error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just $\lceil \log_2(\frac{M^2}{8}-\frac{M}{4}+2)\rceil + 1$ bits, for the M-PSK case.Comment: 12 pages; 11 figure

PASTA: Python Algorithms for Searching Transition stAtes

Chemical reactions are often associated with an energy barrier along the reaction pathway which hinders the spontaneity of the reaction. Changing the energy barrier along the reaction pathway allows one to modulate the performance of a reaction. We present a module, Python Algorithms for Searching Transition stAtes (PASTA), to calculate the energy barrier and locate the transition state of a reaction efficiently. The module is written in python and can perform nudged elastic band, climbing image nudged elastic band and automated nudged elastic band calculations. These methods require the knowledge of the potential energy surface (and its gradient along some direction). This module is written such that it works in conjunction with density functional theory (DFT) codes to obtain this information. Presently it is interfaced with three well known DFT packages: Vienna Ab initio Simulation Package (VASP), Quantum Espresso and Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA). This module is easily extendable and can be interfaced with other DFT, force-field or empirical potential based codes. The uniqueness of the module lies in its user-friendliness. For users with limited computing resources, this module will be an effective tool as it allows to perform the calculations image by image. On the other hand, users with plentiful computing resources (such as users in a high performance computing environment) can perform the calculations for large number of images simultaneously. This module gives users complete flexibility, thereby enabling them to perform calculations on large systems making the best use of the available resources

Inverse scattering method and vector higher order nonlinear Schrodinger equation

A generalised inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrodinger equation, proposed by us. It has been shown that under suitable reduction, vector higher order nonlinear Schrodinger equation reduces to higher order nonlinear Schrodinger equation. The infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equation. A gauge equivalence is shown between the vector higher order nonlinear Schrodinger equation and the generalized Landau Lifshitz equation and the Lax pair for the latter equation has also been constructed in terms of the spin field, establishing direct integrability of the spin system.Comment: 28 page