Quadratic bundle and nonlinear equations

DOI10.1007/BF01029043zbMath0454.35071MaRDI QIDQ1149570

Petr P. Kulish, Vladimir S. Gerdjikov, Maxim I. Ivanov

Publication date: 1981

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationnonlinear equationsnonlinear evolution equationsquadratic bundleinverse scattering technique

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99) Scattering theory of linear operators (47A40)

Related Items (20)

Hamiltonian structures of nonlinear evolution equations connected with a polynomial pencil ⋮ Modeling adiabatic \(N\)-soliton interactions and perturbations ⋮ Solvability of the derivative nonlinear Schrödinger equation and the massive Thirring model ⋮ Long-time asymptotic for the derivative nonlinear Schrödinger equation with step-like initial value ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ The Fokas–Lenells equations: Bilinear approach ⋮ Tau‐function formulation for bright, dark soliton and breather solutions to the massive Thirring model ⋮ Kulish-Sklyanin-type models: integrability and reductions ⋮ Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras \(D_4^{(1)}\), \(D_4^{(2)}\), and \(D_4^{(3)}\) ⋮ Admissible boundary values for the Gerdjikov-Ivanov equation with asymptotically time-periodic boundary data ⋮ Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces ⋮ Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish ⋮ Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem ⋮ Multi-component Gerdjikov-Ivanov system and its Riemann-Hilbert problem under zero boundary conditions ⋮ Reduced D-Kaup–Newell soliton hierarchies from sl(2,ℝ) and so(3,ℝ) ⋮ New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems ⋮ Expansion in squares of the eigenfunctions of a matrix linear system ⋮ Systematic method of generating new integrable systems via inverse Miura maps ⋮ NLS-type equations from quadratic pencil of Lax operators: negative flows ⋮ An integrodifferential Dirac equation with quantized charge in one space dimension

Cites Work

• Closure of the squared Zakharov-Shabat eigenstates
• Evolution equations, singular dispersion relations, and moving eigenvalues
• An exact solution for a derivative nonlinear Schrödinger equation
• Unnamed Item

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