New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schrödinger equation via \(\bar \partial\)-dressing method
From MaRDI portal
Publication:1811468
DOI10.1016/S0375-9601(03)00715-1zbMath1028.35135MaRDI QIDQ1811468
I. B. Formusatik, V. G. Dubrovskij
Publication date: 11 June 2003
Published in: Physics Letters. A (Search for Journal in Brave)
NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20)
Related Items (3)
New exact solutions with functional parameters of the Nizhnik-Veselov-Novikov equation with constant asymptotic values at infinity ⋮ Lump-type wave and interaction solutions of the Bogoyavlenskii-Kadomtsev-Petviashvili equation ⋮ The Gould-Hopper polynomials in the Novikov-Veselov equation
Cites Work
- Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation
- 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
- The D-bar approach to inverse scattering and nonlinear evolutions
- Multiple pole solutions of the nonlinear Schrödinger equation
- Two-dimensional ``inverse scattering problem for negative energies and generalized-analytic functions. I: Energies below the ground state
- The dressing method and nonlocal Riemann-Hilbert problems
- Inverse scattering problem for the two-dimensional Schrödinger operator, the \({\bar\partial}\)-method and nonlinear equations
- Nontrivial scattering of localized solitons in a \((2+1)\)-dimensional integrable system
- Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction
- 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
- Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity
- 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
- Solutions to the Time Dependent Schrödinger and the Kadomtsev-Petviashvili Equations
- Linear spectral problems, non-linear equations and the δ-method
- The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
- Construction of solutions of the sine-Gordon equation by means of Fredholm determinants
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schrödinger equation via \(\bar \partial\)-dressing method