No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions

### Abstract

An integrable generalisation of a Davey-Stewartson type system of two equations involving two scalar functions in 4+2, i.e., in four spatial and two temporal dimensions, has been recently derived by one of the authors. Here, we first show that there exists a reduction of this system to a single equation involving a scalar function in 4+2; we will refer to this equation as the 4+2 Davey-Stewartson equation. We then show that it is possible to reduce this equation to an equation in 3+1, which we will refer to as the 3+1 Davey-Stewartson equation. Furthermore, by employing the so-called direct linearising method, we compute 1- and 2-soliton solutions for both the 4+2 and the 3+1 Davey-Stewartson equations.

© 2013 AIP Publishing LLC

Received 19 December 2012
Accepted 18 July 2013
Published online 13 August 2013

Acknowledgments:
A. S. Fokas was partially supported by EPSRC, as well as the Guggenheim Foundation, USA. The authors are deeply grateful to Jonatan Lenells for many useful suggestions.

Article outline:

I. INTRODUCTION
II. THE DIRECT LINEARISING METHOD IN 4+2
III. THE DIRECT LINEARISING METHOD IN 3+1
IV. SOLITON SOLUTIONS FOR THE 4+2 DS SYSTEM AND FOR THE 4+2 DS EQUATION
A. A 1-soliton solution for the 4+2 DS system
B. A 2-soliton solution for the 4+2 DS system
C. A 1-soliton solution for the 4+2 DS equation
D. A 2-soliton solution for the 4+2 DS equation
V. SOLITON SOLUTIONS FOR THE 3+1 DS SYSTEM AND FOR THE 3+1 DS EQUATION
A. A 1-soliton solution for the 3+1 DS system
B. A 2-soliton solution for the 3+1 DS system
C. A 1-soliton solution for the 3+1 DS equation
D. A 2-soliton solution for the 3+1 DS equation
VI. ANALYSIS OF THE SOLITON SOLUTIONS
A. The 1-soliton solution for the 4+2 DS system
B. The 2-soliton solution for the 4+2 DS system
C. The 1-soliton solution for the 4+2 DS equation
D. The 2-soliton solution for the 4+2 DS equation
E. The 1-soliton solution for the 3+1 DS system
F. The 2-soliton solution for the 3+1 DS system
G. The 1-soliton solution for the 3+1 DS equation
H. The 2-soliton solution for the 3+1 DS equation

/content/aip/journal/jmp/54/8/10.1063/1.4817345

http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/8/10.1063/1.4817345

Article metrics loading...

/content/aip/journal/jmp/54/8/10.1063/1.4817345

2013-08-13

2016-09-27

Full text loading...

###
Most read this month

Article

content/aip/journal/jmp

Journal

5

3

Commenting has been disabled for this content