Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations
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Publication:5955482
DOI10.1016/S0375-9601(02)00033-6zbMath0981.35064MaRDI QIDQ5955482
Publication date: 13 February 2002
Published in: Physics Letters. A (Search for Journal in Brave)
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
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Cites Work
- Unnamed Item
- Similarity methods for differential equations
- Two new applications of the homogeneous balance method
- Exact solutions for a compound KdV-Burgers equation
- Slowly varying solitary waves. I. Korteweg-de Vries equation
- New similarity reductions of the Boussinesq equation
- New similarity solutions for the modified Boussinesq equation
- The Painlevé property for partial differential equations
- On classes of integrable systems and the Painlevé property
- Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg–de Vries equation. I
- A variable coefficient Korteweg–de Vries equation: Similarity analysis and exact solution. II
- Painlevé property, auto-Bäcklund transformation, Lax pairs, and reduction to the standard form for the Korteweg–De Vries equation with nonuniformities
