Multidimensional nonlinear evolution equations and inverse scattering

DOI10.1016/0167-2789(86)90183-1zbMath0604.35070OpenAlexW2010603686MaRDI QIDQ1083618

Adrian I. Nachman, Mark J. Ablowitz

Publication date: 1986

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(86)90183-1

zbMATH Keywords

surveynonlinear evolution equationsinverse scatteringKadomtsev-Petviashvili equationcomplete solvability

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (14)

The D-Bar Method for Diffuse Optical Tomography: A Computational Study ⋮ A New Class of Soliton Solutions for the (Modified) Kadomtsev-Petviashvili Equation ⋮ Mapping Properties of the Nonlinear Fourier Transform in Dimension Two ⋮ On the Kadomtsev-Petviashvili Equation and Associated Constraints ⋮ Exact traveling and non-traveling wave solutions of the time fractional reaction-diffusion equation ⋮ Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps ⋮ A \(\overline{\partial } \)-dressing method for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation ⋮ The Novikov-Veselov equation and the inverse scattering method. I: Analysis ⋮ Unnamed Item ⋮ 3D inverse scattering ⋮ Solving the initial value problem for the 3-wave interaction equations in multidimensions ⋮ Kadomtsev-Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1 ⋮ Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation ⋮ Considerations on conserved quantities and boundary conditions of the \(2 + 1\)-dimensional nonlinear Schrödinger equation

Cites Work

• On the initial value problem of the second Painleve transcendent
• The inverse scattering solution for the full three dimensional three-wave resonant interaction
• The inverse problem for a general \(n \times n\) spectral equation
• Multidimensional Inverse Scattering for First-Order Systems
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• Scattering and inverse scattering for first order systems
• The inverse scattering transform: Semi-infinite interval
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems

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