Nonlocal integrable PDEs from hierarchies of symmetry laws: the example of Pohlmeyer-Lund-Regge equation and its reflectionless potential solutions

DOI10.1016/j.geomphys.2018.01.020zbMath1406.35018OpenAlexW2789695739MaRDI QIDQ1745684

Francesco Demontis, Giovanni Ortenzi, Cornelis V. M. van der Mee

Publication date: 18 April 2018

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2018.01.020

zbMATH Keywords

integrable systemsinverse scattering methodbi-Hamiltonian pencilhierarchies of commuting flowsnonlocal PDEs

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items

Multi-place physics and multi-place nonlocal systems

Cites Work

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• Solitons of the sine-Gordon equation coming in clusters.
• On the higher Poisson structures of the Camassa-Holm hierarchy
• Minimal factorization of matrix and operator functions
• On a construction of multi-soliton solutions of the Pohlmeyer-Lund-Regge system and the classical massive Thirring model
• Separation of variables for bi-Hamiltonian systems
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Exact solutions of the Hirota equation and vortex filaments motion
• The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
• Symmetries for exact solutions to the nonlinear Schrödinger equation
• Explicit solutions to the Korteweg–de Vries equation on the half line
• A simple model of the integrable Hamiltonian equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Local geometric invariants of integrable evolution equations
• The localized induction hierarchy and the Lund - Regge equation
• Unified approach to strings and vortices with soliton solutions
• Exact solutions to the sine-Gordon equation
• Exact solutions to the focusing nonlinear Schrödinger equation
• Explicit solutions of the cubic matrix nonlinear Schrödinger equation
• Three-dimensional distortions of a vortex filament with axial velocity
• On the local systems Hamiltonian in the weakly non-local Poisson brackets