scholarly journals Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

2009 ◽  
Vol 42 (40) ◽  
pp. 404005 ◽  
Author(s):  
Frank Nijhoff ◽  
James Atkinson ◽  
Jarmo Hietarinta
Keyword(s):  
Soliton Solutions ◽  
Matrix Approach ◽  
Cauchy Matrix

scholarly journals EXACT SOLUTIONS TO LATTICE BOUSSINESQ-TYPE EQUATIONS

2012 ◽  
Vol 19 (04) ◽  
pp. 1250031 ◽  
Author(s):  
WEI FENG ◽  
SONG-LIN ZHAO ◽  
DA-JUN ZHANG
Keyword(s):  
Plane Wave ◽  
Exact Solutions ◽  
General Condition ◽  
Soliton Solutions ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Mixed Solutions ◽  
All Solutions ◽  
Condition Equation

In this paper several kinds of exact solutions to lattice Boussinesq-type equations are constructed by means of generalized Cauchy matrix approach, including soliton solutions and mixed solutions. The introduction of the general condition equation set yields that all solutions contain two kinds of plane-wave factors.

Generalized Cauchy matrix approach for lattice Boussinesq-type equations

2012 ◽  
Vol 33 (2) ◽  
pp. 259-270 ◽  
Author(s):  
Songlin Zhao ◽  
Dajun Zhang ◽  
Ying Shi
Keyword(s):  
Matrix Approach ◽  
Cauchy Matrix

A Discrete Negative Order Potential Korteweg–de Vries Equation

2016 ◽  
Vol 71 (12) ◽  
pp. 1151-1158 ◽  
Author(s):  
Song-lin Zhao ◽  
Ying-ying Sun
Keyword(s):  
Exact Solutions ◽  
Vries Equation ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Negative Order ◽  
De Vries ◽  
Continuous Equation ◽  
Multisoliton Solutions ◽  
The Continuum

AbstractWe investigate a discrete negative order potential Korteweg–de Vries (npKdV) equation via the generalised Cauchy matrix approach. Solutions more than multisoliton solutions of this equation are derived by solving the determining equation set. We also show the semidiscrete equation and continuous equation together with their exact solutions by considering the continuum limits.

Discrete and Semidiscrete Models for AKNS Equation

2017 ◽  
Vol 72 (3) ◽  
pp. 281-290 ◽  
Author(s):  
Song-lin Zhao ◽  
Ying Shi
Keyword(s):  
Discrete Model ◽  
Continuum Limit ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Akns Equation

AbstractWe establish a discrete model for the Ablowitz–Kaup–Newell–Segur (AKNS) equation via generalised Cauchy matrix approach. Two semidiscrete AKNS equations are obtained by, respectively, introducing straight continuum limit and skew continuum limit. Some reductions are also discussed.

Oscillatory Solutions for Lattice Korteweg-de Vries-Type Equations

2018 ◽  
Vol 73 (2) ◽  
pp. 91-98
Author(s):  
Wei Feng ◽  
Song-Lin Zhao
Keyword(s):  
Vries Equation ◽  
Sylvester Equation ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Oscillatory Solutions ◽  
Lattice Potential ◽  
De Vries

AbstractBy imposing some shift relations on r which satisfies the Sylvester equation KM+MK=rtc, oscillatory solutions are presented for some lattice Korteweg-de Vries-type equations, including the lattice potential Korteweg de-Vires equation, lattice potential modified Korteweg de-Vires equation, and lattice Schwarzian Korteweg-de Vries equation. This is done through the generalised Cauchy matrix approach.

scholarly journals Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach

2013 ◽  
Vol 131 (1) ◽  
pp. 72-103 ◽  
Author(s):  
D.-J. Zhang ◽  
S.-L. Zhao
Keyword(s):  
Matrix Approach ◽  
Cauchy Matrix

Multi-soliton solutions and the Cauchy matrix scheme

2016 ◽  
pp. 250-279
Author(s):  
J. Hietarinta ◽  
N. Joshi ◽  
F. W. Nijhoff
Keyword(s):  
Soliton Solutions ◽  
Cauchy Matrix ◽  
Matrix Scheme
Sign in / Sign up

Export Citation Format

Share Document