Nonlinear Fourier transforms, integrability and nonlocality in multidimensions

DOI10.1088/0951-7715/20/9/005zbMath1155.35434OpenAlexW2013985944MaRDI QIDQ5421397

Athanassios S. Fokas

Publication date: 22 October 2007

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/20/9/005

zbMATH Keywords

Davey-Stewartson equationnonlocal Riemann-Hilbert problemnonlocal \(d\)-bar problem

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Transform methods (e.g., integral transforms) applied to PDEs (35A22) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (7)

Reduction in the \((4+1)\)-dimensional Fokas equation and their solutions ⋮ A novel \((2 + 1)\)-dimensional nonlinear Schrödinger equation deformed from \((1 + 1)\)-dimensional nonlinear Schrödinger equation ⋮ Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions ⋮ Solving the initial value problem for the 3-wave interaction equations in multidimensions ⋮ Complexification and integrability in multidimensions ⋮ Kadomtsev-Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1 ⋮ Linearisable nonlinear partial differential equations in multidimensions

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