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arXiv:1510.02878 · Communications in Nonlinear Science and Numerical Simulation

Explicit construction of single input–single output logic gates from three soliton solution of Manakov system

M. Vijayajayanthi, Thambithurai Kanna, M. Lakshmanan, K. Murali

Published Dec 24, 2015• 15 citations
arXivHTMLPDF
DOI
10.1016/j.cnsns.2015.12.012

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quant-pharXiv:2606.27569•Jun 29, 2026
By encoding the digital input of a classical logic gate on the Hamiltonian of a quantum system and driving the logic operation by preparing it in the same nonstationary state whatever the input, NOR and NAND classical logic gates are designed with a minimum of three quantum states. The outputs of one gate are obtained either by measuring the distance between the $\ensuremath{\rho}(t)$ periodic quantum trajectory and the output target state ${\ensuremath{\rho}}_{b}$, or by measuring the secular frequency of the $\ensuremath{\rho}(t)$ almost periodic trajectory in the ${\ensuremath{\rho}}_{b}$ direction. A comparison of the stability to noise between the two approaches demonstrates that the frequency approach is more immune to random fluctuations in the Hamiltonian than a distance control approach, opening the way to determine the logic output using a tunneling current passing through the gate.
Abstract We find a restrictive integrable reduction for the one-dimensional spin-orbit-coupled spin-1 Bose-Einstein condensate system, which allows us to reduce the three-component Gross-Pitaevskii system into the two-component Manakov system or the single cubic Schrödinger equation. Based on the reduction, we obtain the multi-breathers, higher-order rouge waves and multi-dark soliton solutions for ferromagnetic and anti-ferromagnetic system, respectively. Furthermore, the impacts of the spin-orbit coupling to the multi-soliton dynamics, and the stability of these soliton solutions have also been discussed.
Multicomponent nonlinear Schrödinger equations constitute fundamental models for coherent matter waves in multicomponent Bose--Einstein condensates, spinor quantum fluids, and vector nonlinear optical systems. We develop a vector formulation of the Hirota bilinear formalism for the completely integrable Manakov system that treats the coupled nonlinear Schrödinger equations directly at the vector level rather than through the conventional component-wise decomposition. This framework naturally retains the intrinsic multicomponent representation of the model while providing compact analytical expressions for exact vector soliton solutions. Within this approach, we systematically construct bright, dark, and mixed one-, two-, and three-soliton solutions and show how the underlying vector structure provides a unified description of their nonlinear interactions. In particular, the proposed formalism makes the coupling between the different components explicit while preserving the geometric organization of the vector system throughout the bilinearization procedure. Beyond its analytical simplicity, the framework offers a natural perspective for the study of coherent multicomponent nonlinear excitations and provides a foundation for extending vector Hirota methods to other classes of exact solutions, including rogue waves, periodic waves, and rational solutions.