Soliton multidimensional equations and integrable evolutions preserving Laplace's equation

DOI10.1016/J.PHYSLETA.2007.09.037zbMath1217.35160OpenAlexW2147791877MaRDI QIDQ552836

Athanassios S. Fokas

Publication date: 26 July 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2007.09.037

zbMATH Keywords

Kadomzev-Pedviashwili equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Wave equation (35L05) Soliton equations (35Q51) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

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 ⋮ Complexification and integrability in multidimensions ⋮ Kadomtsev-Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1 ⋮ Linearisable nonlinear partial differential equations in multidimensions ⋮ Integrability of the modified generalised Vakhnenko equation

Cites Work

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• Integrable Nonlinear Evolution Partial Differential Equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>Dimensions
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• The Dbar formalism for certain linear non-homogeneous elliptic PDEs in two dimensions
• Method for Solving the Korteweg-deVries Equation
• A simple one‐dimensional model for the three‐dimensional vorticity equation

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