Quantum mechanics

Mathematical physics

Lax pair

Materials science

Boundary value problem

Component (thermodynamics)

Schrödinger's cat

Matrix (chemical analysis)

Method of steepest descent

Physics

Nonlinear system

Integrable system

Mathematics

Riemann–Hilbert problem

Mathematical analysis

Composite material

Journal of Geometry and Physics

Starting from a specific example of 4 × 4 matrix spectral problems, an integrable coupled hierarchy, which includes a three-component coupled nonlinear Schrödinger system as the first nonlinear one, is generated, and an associated oscillatory Riemann–Hilbert problem is formulated. With the nonlinear steepest descent method, the leading long-time asymptotics for the Cauchy problem of the three-component coupled nonlinear Schrödinger system is computed, through deforming the oscillatory Riemann–Hilbert problem into a model one which is solvable.

Long-time asymptotics of a three-component coupled nonlinear Schrödinger system