Spectrally accurate space–time solution of Manakov systems

Fast Spectrally-accurate Solution of Variable-coeecient Elliptic Problems

A simple, eecient, spectrally-accurate numerical method for solving variable-coeecient elliptic partial diierential equations in periodic geometry is described. Numerical results show that the method is eecient and accurate even for diicult problems including convection-diiusion equations. Generalizations and applications to phase eld models of crystal growth are discussed.

Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator

The chain collocation method: A spectrally accurate calculus of forms

Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions...

Quantum theory of Manakov solitons

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schrödinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and d...

Generalized Darboux-Manakov-Zakharov Systems and their Application

We introduce the notion of generalized Darboux-Manakov-Zakharov systems of semilinear partial differential equations. ∂ 2u ∂xi∂x j = fi j ( xk,u, ∂u ∂xl ) , 1 ≤ i < j ≤ n, k, l ∈ {1, . . . ,n}. (1) for a real-valued function u(x1, . . . ,xn). These generalize linear systems in the equation class ∂ 2u ∂xi∂x j −Γ j i(x) ∂u ∂xi −Γi j(x) ∂u ∂x j +C(i j)(x)u = 0, 1 ≤ i < j ≤ n, (2) where coefficient...