Keyword

Bäcklund transformations

Description: Bäcklund transformations are mathematical relations that map solutions of differential equations to other solutions, especially in the study of integrable nonlinear systems.

Primary topic: Nonlinear Waves and Solitons (84%)

Related topic: Nonlinear Waves and Solitons (84%)

Wikidata ID: wiki/Q3537515

OpenAlex ID: keywords/backlund-transformations

The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

1974 · Mark J. Ablowitz, David J. Kaup, et al. · Studies in Applied Mathematics · 3,193

Symplectic structures, their Bäcklund transformations and hereditary symmetries

1981 · B. Fuchssteiner, A.S. Fokas · Physica D Nonlinear Phenomena · 1,835

Solitons in Mathematics and Physics

1985 · Alan C. Newell · Society for Industrial and Applied Mathematics eBooks · 1,589

A simple model of the integrable Hamiltonian equation

1978 · Franco Magri · Journal of Mathematical Physics · 1,386

Bäcklund and Darboux Transformations

2002 · C. Rogers, W. K. Schief · Cambridge University Press eBooks · 822

Direct Methods in Soliton Theory

1980 · R. Hirota · Topics in current physics · 808

Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws

1975 · M. Wadati, H. Sanuki, et al. · Progress of Theoretical Physics · 750

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The Korteweg–deVries Equation: A Survey of Results

1976 · Robert M. Miura · SIAM Review · 703

A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo–Miwa equation

2009 · Wen-Xiu Ma, Jyh-Hao Lee · Chaos Solitons & Fractals · 622

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Prolongation structures of nonlinear evolution equations

1975 · H. D. Wahlquist, F. B. Estabrook · Journal of Mathematical Physics · 620

The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative

1983 · John Weiss · Journal of Mathematical Physics · 581

Bäcklund Transformation for Solutions of the Korteweg-de Vries Equation

1973 · Hugo D. Wahlquist, Frank B. Estabrook · Physical Review Letters · 508

Bäcklund Transformations and Their Applications

1982 · Mathematics in Science and Engineering/Mathematics in science and engineering · 506

Rational Surfaces Associated with Affine Root Systems¶and Geometry of the Painlevé Equations

2001 · Hidetaka Sakai · Communications in Mathematical Physics · 501

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Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation

1996 · Benno Fuchssteiner · Physica D Nonlinear Phenomena · 494

Discrete Analogue of a Generalized Toda Equation

1981 · Ryogo Hirota · Journal of the Physical Society of Japan · 491

Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique

1983 · N.C. Freeman, J.J.C. Nimmo · Physics Letters A · 489

Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation

1996 · W.X. Ma, B. Fuchssteiner · International Journal of Non-Linear Mechanics · 459

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Harmonic maps into Lie groups: classical solutions of the chiral model

1989 · Karen Uhlenbeck · Journal of Differential Geometry · 440

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A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem

1974 · R. Hirota · Progress of Theoretical Physics · 426

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Wave Propagation in Nonlinear Lattice. I

1975 · Miki Wadati · Journal of the Physical Society of Japan · 413

Prolongation structures of nonlinear evolution equations. II

1976 · F. B. Estabrook, H. D. Wahlquist · Journal of Mathematical Physics · 405

Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation

1996 · W. X. Ma, B. Fuchssteiner · 403

Integrability, Self-Duality, and Twistor Theory

1996 · L J Mason, N M J Woodhouse · 386

An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders

1980 · Masaaki Ito · Journal of the Physical Society of Japan · 378

Works count: 4,122

Citation count: 76,680