Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy
DOI10.13108/2021-13-2-81zbMath1488.37055OpenAlexW3190119363MaRDI QIDQ5155558
Vladimir B. Matveev, Aleksandr Olegovich Smirnov
Publication date: 7 October 2021
Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)
Full work available at URL: http://mathnet.ru/eng/ufa566
nonlinear Schrödinger equationtheta functionPT-symmetrynonlocal equationspectral curvefinite-gap solutionAblowitz-Kaup-Newell-Segur hierarchy
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)
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Cites Work
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- Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves
- General \(N\)-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
- Reductions of Darboux transformations for the \(\mathcal{PT}\)-symmetric nonlocal Davey-Stewartson equations
- Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation
- Rational solutions for the nonlocal sixth-order nonlinear Schrödinger equation
- Rational and semi-rational solutions of the \(y\)-nonlocal Davey-Stewartson I equation
- Rogue waves in the nonlocal \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equation
- Semi-rational solutions for the \((2 + 1)\)-dimensional nonlocal Fokas system
- General soliton solutions to a \((2+1)\)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
- Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
- Theta functions on Riemann surfaces
- Two \((2+1)\)-dimensional integrable nonlocal nonlinear Schrödinger equations: breather, rational and semi-rational solutions
- Two-phase periodic solutions to the AKNS hierarchy equations
- New classes of solutions in the coupled \(\mathcal{PT}\) symmetric nonlocal nonlinear Schrödinger equations with four wave mixing
- Nonlocal modified KdV equations and their soliton solutions by Hirota method
- Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system
- Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation
- Rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schrödinger equations
- Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: general analysis and simplest examples
- Exact solutions of nonlocal Fokas-Lenells equation
- Darboux transformations and exact solutions for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation
- On general rogue waves in the parity-time-symmetric nonlinear Schrödinger equation
- Three-phase freak waves
- Periodic two-phase ``rogue waves
- The \(N\)-wave equations with \(\mathcal{PT}\) symmetry
- Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
- Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening
- Theta functions and non-linear equations
- A MATRIX ANALOGUE OF APPELL'S THEOREM AND REDUCTIONS OF MULTIDIMENSIONAL RIEMANN THETA-FUNCTIONS
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- Rogue waves of the nonlocal Davey–Stewartson I equation
- Integrable Nonlocal Nonlinear Equations
- Deformation of dark solitons in a PT-invariant variable coefficients nonlocal nonlinear Schrödinger equation
- AKNS and NLS hierarchies, MRW solutions, P n breathers, and beyond
- Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions
- On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain
- Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy
- Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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