2 citations · 2 across the 2 of their papers we have counts for
5 papers
Continuous and Discrete Homotopy Operators with Applications in Integrability Testing
Willy Hereman, Michael Colagrosso, Ryan Sayers +4
We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D ge…
Computing Riemann Theta Functions
Bernard Deconinck, Matthias Heil, Alexander Bobenko +2
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathemati…
Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential
Bernard Deconinck, Bela A. Frigyik, J. Nathan Kutz
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are c…
Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation
Bernard Deconinck, Harvey Segur
The real, nonsingular elliptic solutions of the Korteweg-deVries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is…
Canonical variables for multiphase solutions of the KP equation
Bernard Deconinck
The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional…