𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A note on solutions of the Korteweg–de Vries hierarchy

✍ Scribed by Nikolay A. Kudryashov

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
158 KB
Volume
16
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

Solutions of the Korteweg-de Vries hierarchy are discussed. It is shown that results by Wazwaz [Wazwaz AM. Multiple-soliton solutions of the perturbed KdV equation. Commun Nonlinear Sci Simul 2010;15(11):3270-73] are the well-known consequences of the full integrability for the Korteweg-de Vries hierarchy.

📜 SIMILAR VOLUMES

A New Explicit Expression for the Kortew
A New Explicit Expression for the Korteweg – De Vries Hierarchy
✍ Ivan Avramidi; Rainer Schimming 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 222 KB

We derive an improved fully explicit expression for the right -hand sides of the matrix KdV hierarchy using the relation to the heat kernel of the one -dimensional Schrödinger operator. Our method of "matrix elements" produces, moreover, an explicit expression for the powers of a Schrödinger-like d

The coupling integrable couplings of the
The coupling integrable couplings of the modified Korteweg–de Vries (mKdV) hierarchy
✍ Xiurong Guo 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 223 KB

a b s t r a c t Two kinds of coupling integrable couplings of the mKdV hierarchy are obtained, respectively, by making use of two higher-dimensional Lie algebras in the vector forms. The Hamiltonian structure of one reduced coupling integrable coupling of them is worked out by employing the variatio