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Wronskians, generalized Wronskians and solutions to the Korteweg–de Vries equation

✍ Scribed by Wen-Xiu Ma

Book ID
104363383
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
441 KB
Volume
19
Category
Article
ISSN
0960-0779

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✦ Synopsis

A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries (KdV) equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the KdV equation. Moreover, general positons and negatons are constructed through the Wronskian formulation. A few new exact solutions to the KdV equation are explicitly presented as examples of Wronskian solutions.

📜 SIMILAR VOLUMES

Large Time Asymptotics of Solutions to t
Large Time Asymptotics of Solutions to the Generalized Korteweg–de Vries Equation
✍ Nakao Hayashi; Pavel I. Naumkin 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 389 KB

We study the asymptotic behavior for large time of solutions to the Cauchy problem for the generalized Korteweg de Vries (gKdV) equation u t + ( |u| \&1 u) x + 1 3 u xxx =0, where x, t # R when the initial data are small enough. If the power \ of the nonlinearity is greater than 3 then the solution