\( \bar\partial \)-dressing method for a few \((2+1)\)-dimensional integrable coupling systems
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Publication:2056815
DOI10.1134/S0040577921090063zbMath1482.81040OpenAlexW3201783644MaRDI QIDQ2056815
Publication date: 8 December 2021
Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1134/s0040577921090063
exact solutionintegrable coupling system\( \bar\partial \)-dressing methodinverse spectral transform method
Model quantum field theories (81T10) Inverse scattering problems in quantum theory (81U40) Exactly and quasi-solvable systems arising in quantum theory (81U15) Special quantum systems, such as solvable systems (81Q80)
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The \(\bar{\partial}\)-dressing method for the (2+1)-dimensional Konopelchenko-Dubrovsky equation, A new multi-component integrable coupling and its application to isospectral and nonisospectral problems
Cites Work
- Unnamed Item
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- A few continuous and discrete dynamical systems
- The AB equations and the \(\bar\partial\)-dressing method in semi-characteristic coordinates
- A few integrable systems and spatial spectral transformations
- Integrable theory of the perturbation equations.
- An integrable coupling hierarchy of the MKdV\_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy
- Semi-direct sums of Lie algebras and continuous integrable couplings
- The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
- Construction of higher-dimensional nonlinear integrable systems and of their solutions
- Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
- Bäcklund transformations and their applications
- Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy
- Long-time asymptotics and the bright \(N\)-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach
- A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system
- \( \overline{\partial} \)-dressing method for the coupled Gerdjikov-Ivanov equation
- Long-time asymptotic behavior for the complex short pulse equation
- Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method
- Two integrable couplings of a generalized d-Kaup-Newell hierarchy and their Hamiltonian and bi-Hamiltonian structures
- Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy
- A simple method for generating integrable hierarchies with multi-potential functions
- The construction of exact rational solutions with constant asymptotic values at infinity of two-dimensional NVN integrable nonlinear evolution equations via the $\overline{\partial}$-dressing method
- Reduced D-Kaup–Newell soliton hierarchies from sl(2,ℝ) and so(3,ℝ)
- Integrable two-dimensional generalisation of the sine- and sinh-Gordon equations
- On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
- APPLICATIONS OF THE LIE ALGEBRA gl(2)
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
- The two-dimensional second-order differential spectral problem: compatibility conditions, general BTs and integrable equations
- The Painlevé property for partial differential equations
- Spectral transform for a two spatial dimension extension of the dispersive long wave equation
- The non-local delta problem and (2+1)-dimensional soliton equations
- The construction of exact multiple pole solutions of some (2+1)-dimensional integrable nonlinear evolution equations via the -dressing method
- A steepest descent method for oscillatory Riemann-Hilbert problems
- The application of the -dressing method to some integrable -dimensional nonlinear equations
- Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
- Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling
- A novel kind of AKNS integrable couplings and their Hamiltonian structures
- A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
- A hierarchy of coupled evolution equations with self-consistent sources and the dressing method
- Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
- Darboux Transformations
- Exact envelope-soliton solutions of a nonlinear wave equation
- Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy
