Effective integration of the nonlinear vector Schrödinger equation

DOI10.1016/j.physd.2006.10.005zbMath1121.35129arXivmath-ph/0501072OpenAlexW2034576891MaRDI QIDQ870849

J. N. Elgin, Alexander R. Its, Viktor Z.Enol'skij

Publication date: 15 March 2007

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0501072

zbMATH Keywords

trigonal curveManakov systemfinite gap solutionsJacobian \(\vartheta\)-functions

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (12)

Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation ⋮ The vector nonlinear Schrödinger hierarchy ⋮ Breather solutions to the AB system with non-zero background ⋮ Application of the trigonal curve to a hierarchy of generalized Toda lattices ⋮ The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws ⋮ Turbulence and shock-waves in crowd dynamics ⋮ Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy ⋮ Collision dynamics of elliptically polarized solitons in coupled nonlinear Schrödinger equations ⋮ On elliptic solutions of a coupled nonlinear Schrödinger system ⋮ The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy ⋮ Algebro-geometric solutions to the Manakov hierarchy ⋮ Algebro-geometric solutions to the modified Sawada-Kotera hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation
• On the zeros of the Weierstrass \(\wp\)-function
• On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems
• Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDE's
• On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system
• On directional derivatives of the theta function along its divisor
• The stationary equations of a coupled nonlinear Schrödinger system
• Theta functions on Riemann surfaces
• Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
• Quasi–periodic and periodic solutions for coupled nonlinear Schrödinger equations of Manakov type
• Quasiperiodic solutions for matrix nonlinear Schrödinger equations
• Matrix nonlinear Schrödinger equations and moment maps into loop algebras
• The spectral theory of a functional-difference operator in conformal field theory
• Computing Riemann matrices of algebraic curves

This page was built for publication: Effective integration of the nonlinear vector Schrödinger equation