Elementary Bäcklund transformations, nonlinear superposition formulae and algebraic construction of solutions for the nonlinear evolution equations solvable by the Zakharov-Shabat spectral transform

DOI10.1016/0167-2789(84)90007-1zbMath0596.35009OpenAlexW2008218944MaRDI QIDQ1078394

Francesco Calogero, Antonio Degasperis

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0167-2789(84)90007-1

zbMATH Keywords

Bäcklund transformationsnonlinear evolution equationsKorteweg-de Vries equationsnonlinear superpositions

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Solutions to PDEs in closed form (35C05)

Related Items (8)

Soliton-like solutions for a nonisospectral KdV hierarchy ⋮ A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems ⋮ Formation of solitons from the Langmuir waves with random phases ⋮ Soliton structure versus singularity analysis: Third-order completely integrable nonlinear differential equations in \(1+1\)-dimensions ⋮ Dromions and a boundary value problem for the Davey-Stewartson 1 equation ⋮ Integration of the matrix KdV equation with self-consistent source ⋮ Systematic method of generating new integrable systems via inverse Miura maps ⋮ The higher-order KdV equation with a source and nonlinear superposition formula.

Cites Work

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• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On the general structure of nonlinear evolution equations and their Backlund transformations connected with the matrix non-stationary Schrodinger spectral problem

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