Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

DOI10.1063/1.4940996zbMath1342.35356arXiv1410.5350OpenAlexW1700240687MaRDI QIDQ2795518

Tihomir I. Valchev

Publication date: 21 March 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5350

zbMATH Keywords

nonlinear Schrödinger equationHermitian symmetric spacesrational solutionssoliton type solutionsZakharov-Shabat's dressing procedure

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Soliton solutions (35C08)

Related Items (2)

On integrable wave interactions and Lax pairs on symmetric spaces ⋮ Multi-component Gerdjikov-Ivanov system and its Riemann-Hilbert problem under zero boundary conditions

Cites Work

• Unnamed Item
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• Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces
• Waves that appear from nowhere and disappear without a trace
• Solutions of multi-component NLS models and spinor Bose-Einstein condensates
• What makes the Peregrine soliton so special as a prototype of freak waves?
• The reduction problem and the inverse scattering method
• On spectral theory of Lax operators on symmetric spaces: vanishing versus constant boundary conditions
• Nonlinear Schrödinger equations and simple Lie algebras
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• On the quadratic bundles related to Hermitian symmetric spaces
• Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
• The Darboux transformation of the derivative nonlinear Schrödinger equation
• Rogue waves, rational solutions, the patterns of their zeros and integral relations
• Derivative nonlinear Schrodinger equations and Hermitian symmetric spaces
• Generalised KdV and MKdV equations associated with symmetric spaces
• An exact solution for a derivative nonlinear Schrödinger equation
• Crum transformation and rational solutions of the non-focusing nonlinear Schrödinger equation
• The hierarchy of multi-soliton solutions of the derivative nonlinear Schr dinger equation
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• Complete integrability of derivative nonlinear Schrödinger-type equations
• Integrable Hamiltonian hierarchies. Spectral and geometric methods

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