Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system

✍ Scribed by Xing-Biao Hu; Dao-Liu Wang; Hon-Wah Tam

• Book ID: 104349063
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 196 KB
• Volume: 13
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(00)00052-5

✦ Synopsis

A coupled Raxnani equation and its related system axe proposed. By dependent variable transformation, they are transformed into bilinear equations. Lax pairs and B/icklund transformations axe presented for these two systems. Soliton solutions and rational solutions to the systems could be obtained. (~) 2000 Elsevier Science Ltd. All rights reserved.

Keywords--Solitons, Integrable systems, Lax pairs, B/~cklund transformations.

It is known that many integrable models have played an important role in applied sciences. No doubt, it is one of central topics in soliton theory to search for as many integrable systems as possible. An effective way of seeking new integrable systems is to find integrable extensions of the known integrable systems. For example, for the celebrated KdV equation

several coupled KdV equations have been found (see, e.g., ).

In this letter, we will consider an integrable extension of the following less studied Ramani equation: ~xx~xx + 15u~uxx~ + 15u~u~ + a5~2xU~x --5(~x~xt + 3u~ut + 3u~,) -5~t~ = 0. (1)