Quick search Find article
Quick search
Find article

Soliton solutions for Q3

FREE ARTICLE

James Atkinson1, Jarmo Hietarinta2 and Frank Nijhoff1

Show affiliations


[1]
Ablowitz M J and Ladik F J 1976 A nonlinear difference scheme and inverse scattering Stud. Appl. Math. 55 213-29

 
Ablowitz M J and Ladik F J 1977 On the solution of a class of nonlinear partial difference equations Stud. Appl. Math. 57 1-12

[2]
Hirota R 1977 Nonlinear partial difference equations I-III J. Phys. Soc. Japan 43 1424-33
CrossRef 
 
Hirota R 1977 Nonlinear partial difference equations I-III J. Phys. Soc. Japan 43 2074-89
CrossRef 
[3]
Nijhoff F W, Quispel G R W and Capel H W 1983 Direct linearization of nonlinear difference-difference equations Phys. Lett. 97A 125-8
CrossRef 
[4]
Quispel G R W, Nijhoff F W, Capel H W and van der Linden J 1984 Linear integral equations and nonlinear difference-difference equations Physica 125A 344-80
CrossRef 
[5]
Date E, Jimbo M and Miwa T 1982 Method for generating discrete soliton equations I-II J. Phys. Soc. Japan 51 4116-31
CrossRef 
 
Date E, Jimbo M and Miwa T 1983 Method for generating discrete soliton equations III-V J. Phys. Soc. Japan 52 388-93
CrossRef 
 
Date E, Jimbo M and Miwa T 1983 Method for generating discrete soliton equations III-V J. Phys. Soc. Japan 52 761-71
CrossRef 
[6]
Nijhoff F W and Capel H W 1995 The discrete Korteweg-de Vries equation Acta Appl. Math. 39 133-58
CrossRef 
[7]
Nijhoff F W and Walker A J 2001 The discrete and continuous Painlevé VI hierarchy and the garnier systems Glasgow Math. J. 43A 109-23
CrossRef 
[8]
Bobenko A I and Suris Yu B 2002 Integrable systems on quad-graphs Int. Math. Res. Not. 11 573-611
CrossRef 
[9]
Adler V E, Bobenko A I and Suris Yu B 2002 Classification of integrable equations on quad-graphs, the consistency approach Commun. Math. Phys. 233 513-43

[10]
Adler V E, Bobenko A I and Suris Y B 2007 Discrete Nonlinear Hyperbolic Equations. Classification of Integrable Cases (Preprint 0705.1663)
Preprint 
[11]
Adler V E 1998 Bäcklund transformation for the Krichever-Novikov equation Int. Math. Res. Not. 1 1-4
CrossRef 
[12]
Krichever I M and Novikov S P 1979 Holomorphic fiberings and nonlinear equations Sov. Math.-Dokl. 20 650-4

[13]
Krichever I M and Novikov S P 1981 Holomorphic bundles over algebraic curves and nonlinear equations Russ. Math. Surv. 35 53-79
IOPscience 
[14]
Nijhoff F W 2002 Lax pair for the Adler (lattice Krichever-Novikov) system Phys. Lett. A 297 49-58
CrossRef 
[15]
Adler V E and Suris Yu B 2004 Q4: integrable master equation related to an elliptic curve Int. Math. Res. Not. 47 2523-53
CrossRef 
[16]
Atkinson J, Hietarinta J and Nijhoff F 2007 Seed and soliton solutions of Adler's lattice equation J. Phys. A: Math. Theor. 40 F1-8
IOPscience 
[17]
Atkinson J and Nijhoff F W 2007 Solutions of Adler's lattice equation associated with 2-cycles of the Bäcklund transformation J. Nonlinear Math. Phys. Proc. NEEDS 2007 Conf. (Preprint 0710.2643) at press
Preprint 
[18]
Atkinson J and Nijhoff F W in preparation

[19]
Rasin O G and Hydon P 2006 Conservation laws for NQC-type difference equations J. Phys. A: Math. Gen. 39 14055-66
IOPscience 
[20]
Hirota R 1981 Discrete analogue of a generalized Toda equation J. Phys. Soc. Japan 50 3785-91
CrossRef 
[21]
Miwa T 1982 On Hirota's difference equations Proc. Japan Acad. A 58 9-12
CrossRef 
[22]
Atkinson J 2008 Bäcklund transformations for integrable lattice equations Preprint 0801.1998
Preprint 
[23]
Hearn A C 2004 REDUCE User's Manual, Version 3, 8

crossref member

  1. Soliton solutions for Q3

    James Atkinson et al 2008 J. Phys. A: Math. Theor. 41 142001

  2. Monotonicity of rotation set for toroidal chaos of a resonantly kicked linear oscillator

    Jaroslaw Kwapisz 1998 Nonlinearity 11 547

  3. Challenges for first-principles based properties of defects in semiconductors and oxides

    2009 Modelling Simul. Mater. Sci. Eng. 17 080201

  4. A generalized Lagrange equation in implicit form for non-conservative mechanics

    F Barone et al 1997 J. Phys. A: Math. Gen. 30 1575

  5. Analysis of electron wave functions that exhibit oscillatory behavior at the Bloch frequency

    J N Churchill and F E Holmstrom 1994 Phys. Scr. 50 305

  6. Single-walled carbon nanotube–superconductor entangler: noise correlations and Einstein–Podolsky–Rosen states

    V Bouchiat et al 2003 Nanotechnology 14 77

  7. Muon-catalysed fusion as a finite Markov process

    C DeW Van Siclen 1985 J. Phys. G: Nucl. Phys. 11 267

  8. On the Gibbs paradox: what does indistinguishability really mean?

    A M Lesk 1980 J. Phys. A: Math. Gen. 13 L111

  9. On Birkhoff's theorem for electromagnetic fields in a scalar-tensor theory of gravitation

    D R K Reddy 1977 J. Phys. A: Math. Gen. 10 185

  10. On generalized fractional superstring theory

    H Chakir et al 1997 Class. Quantum Grav. 14 2049

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.