On the \(\bar\partial \)-problem and dressing method for the complex vector modified KdV equation
DOI10.1134/S0040577921110064zbMath1484.37077OpenAlexW3215028193WikidataQ114075191 ScholiaQ114075191MaRDI QIDQ2056849
Shou-Fu Tian, Zhi-Jia Wu, Jia Cheng
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/s0040577921110064
recursion operator\(N\)-soliton solutionvector modified Korteweg-de Vries equation\( \bar\partial \)-dressing method
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
Cites Work
- Unnamed Item
- Unnamed Item
- Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method
- The AB equations and the \(\bar\partial\)-dressing method in semi-characteristic coordinates
- On solutions to the nonlocal \(\overline{\partial}\)-problem and (2+1) dimensional completely integrable systems
- Dromions and a boundary value problem for the Davey-Stewartson 1 equation
- The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
- Nonlinear Schrödinger equations and simple Lie algebras
- Construction of higher-dimensional nonlinear integrable systems and of their solutions
- The D-bar approach to inverse scattering and nonlinear evolutions
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
- An initial-boundary value problem for the Korteweg-de Vries equation
- The Boussinesq equation revisited
- The dressing method and nonlocal Riemann-Hilbert problems
- Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval
- Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system
- \( \overline{\partial} \)-dressing method for the coupled Gerdjikov-Ivanov equation
- Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation
- Application of the Riemann-Hilbert method to the vector modified Korteweg-de Vries equation
- Solutions to the Kaup-Broer system and its \((2+1)\) dimensional integrable generalization via the dressing method
- Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions
- New solutions to the differential-difference KP equation
- Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
- A three-wave interaction model with self-consistent sources: the \(\overline{\partial}\)-dressing method and solutions
- The generalized Dirichlet to Neumann map for the KdV equation on the half-line
- The Coupled Modified Korteweg-de Vries Equations
- A Class of Exactly Solvable Nonlinear Evolution Equations
- The Modified Korteweg-de Vries Equation
- Solutions to the modified Korteweg–de Vries equation
- Hamiltonian formulation of the inverse scattering method of the modified KdV equation under the non-vanishing boundary condition u(x, t) to b as x to +or- infinity
- On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
- Forced (2 + 1)-dimensional discrete three-wave equation
- Generalised KdV and MKdV equations associated with symmetric spaces
- An infinite hierarchy of symmetries associated with hyperbolic surfaces
- The ∂̄-dressing method and the solutions with constant asymptotic values at infinity of DS-II equation
- Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method
- Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
- Linear spectral problems, non-linear equations and the δ-method
- Noncommutative Extension of \bar∂-Dressing Method
- The bound-state soliton solutions of the complex modified KdV equation
- Integrable properties of the general coupled nonlinear Schrödinger equations
This page was built for publication: On the \(\bar\partial \)-problem and dressing method for the complex vector modified KdV equation