𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Quasi-periodic solutions of the 2+1 dimensional modified Korteweg–de Vries equation

✍ Scribed by Xianguo Geng; Cewen Cao

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
88 KB
Volume
261
Category
Article
ISSN
0375-9601

No coin nor oath required. For personal study only.

✦ Synopsis

A new 2 q 1 dimensional modified Korteweg-de Vries equation is proposed and decomposed into the first two members in the well-known Kaup-Newell hierarchy, which are reduced further into integrable ordinary differential equations in the invariant set produced by the stationary Kaup-Newell equation. The Abel-Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the 2 q 1 dimensional modified Korteweg-de Vries equation are obtained in terms of the Riemann theta functions.

📜 SIMILAR VOLUMES

Quasi-periodic waves of the supersymmetr
Quasi-periodic waves of the supersymmetric modified Korteweg–de Vries equation
✍ Lin Luo; Engui Fan 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 340 KB

Based on the Hirota bilinear method and the Riemann theta function, a straightforward way is shown to construct quasi-periodic wave solutions of supersymmetric equations. The resulting theory is applied to the supersymmetric modified Korteweg-de Vries equation. Further, we analyze the asymptotic pro

New variable separation solutions and no
New variable separation solutions and nonlinear phenomena for the (2+1)-dimensional modified Korteweg–de Vries equation
✍ Yueqian Liang; Guangmei Wei; Xiaonan Li 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 781 KB

Variable separation approach, which is a powerful approach in the linear science, has been successfully generalized to the nonlinear science as nonlinear variable separation methods. The (2 + 1)-dimensional modified Korteweg-de Vries (mKdV) equation is hereby investigated, and new variable separatio