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Full-Text Articles in Physical Sciences and Mathematics
Lattice Quantum Algorithm For The Schrodinger Wave Equation In 2+1 Dimensions With A Demonstration By Modeling Soliton Instabilities, Jeffrey Yepez, George Vahala, Linda L. Vahala
Lattice Quantum Algorithm For The Schrodinger Wave Equation In 2+1 Dimensions With A Demonstration By Modeling Soliton Instabilities, Jeffrey Yepez, George Vahala, Linda L. Vahala
Electrical & Computer Engineering Faculty Publications
A lattice-based quantum algorithm is presented to model the non-linear Schrödinger-like equations in 2 + 1 dimensions. In this lattice-based model, using only 2 qubits per node, a sequence of unitary collide (qubit-qubit interaction) and stream (qubit translation) operators locally evolve a discrete field of probability amplitudes that in the long-wavelength limit accurately approximates a non-relativistic scalar wave function. The collision operator locally entangles pairs of qubits followed by a streaming operator that spreads the entanglement throughout the two dimensional lattice. The quantum algorithmic scheme employs a non-linear potential that is proportional to the moduli square of the wave function. …
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov
Articles
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov
Articles
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.