A unified explicit form of Bäcklund transformations for generalized hierarchies of KdV equations
type: Item
instance of: scholarly article
title: A unified explicit form of Bäcklund transformations for generalized hierarchies of KdV equations
zbMATH Open document ID: 0605.35077
DOI: 10.1007/BF00574158
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: In this paper, the authors show that the explicit form of Bäcklund transformations of the KdV equation is universal for the whole hierarchies of KdV equations. These equations are of \((2L+1)th\) order for any integer \(L>0\) and their coefficients may depend on the time variable t. The theorem of permutability and the superposition formulas is obtained in a universal manner. The proof is simpler than that obtained in the conventional way. Hence, the authors obtain a universal expression of solitons whose speed is not generally a constant. Some new facts are presented for \(L>1:\) For instance, the soliton with a large amplitude may have a lower speed. There are solitons which vibrate periodically. The interactions of two solitons may have many modes. Beside the usual case, instead of crossing, there are reflections of solitons or a gluing of solitons. Two solitons may have infinite collisions or keep apart forever.
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3977560
zbMATH Keywords: Bäcklund transformations
zbMATH Keywords: KdV equation
zbMATH Keywords: theorem of permutability
zbMATH Keywords: superposition formulas
zbMATH Keywords: solitons
author: Chao-Hao Gu
author: He-Sheng Hu
MaRDI profile type: Publication
cites work: Lie groups and KdV equations
cites work: Q3034226
full work available at URL: https://doi.org/10.1007/bf00574158
OpenAlex ID: W2019403379
description: scientific article; zbMATH DE number 3977560