ArticlesFree Access

EXACT SOLUTIONS TO LATTICE BOUSSINESQ-TYPE EQUATIONS

WEI FENG

Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069, P. R. China

Search for more papers by this author

SONG-LIN ZHAO

Department of Mathematics, Shanghai University, 99, Shangda Road, Shanghai 200444, P. R. China

Search for more papers by this author

, and

DA-JUN ZHANG

Department of Mathematics, Shanghai University, 99, Shangda Road, Shanghai 200444, P. R. China

Search for more papers by this author

Cited by:0 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 39A14

References

E. Date , M. Jimbo and T. Miwa , J. Phys. Soc. Japan 52 , 388 ( 1983 ) . Crossref, Google Scholar
J. Hietarinta , J. Phys. A: Math. Theor. 44 , 22 ( 2011 ) . Google Scholar
J. Hietarinta and D. J. Zhang , J. Math. Phys. 51 , 12 ( 2010 ) . Crossref, Web of Science, Google Scholar
J. Hietarinta and D. J. Zhang , SIGMA 7 , 14 ( 2011 ) . Web of Science, Google Scholar
R. Hirota , J. Phys. Soc. Japan 50 , 3785 ( 1981 ) . Crossref, Google Scholar
S. B. Lobb and F. W. Nijhoff , J. Phys. A: Math. Theor. 43 , 11 ( 2010 ) . Crossref, Web of Science, Google Scholar
F. W. Nijhoff, Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, eds. A. S. Fokas and I. M. Gel'fand (Birkhäuser Verlag, 1996) pp. 237–260. Google Scholar
F. W. Nijhoff, Discrete Integrable Geometry and Physics, eds. A. I. Bobenko and R. Seiler (Clarendon Press, Oxford, 1999) pp. 209–234. Google Scholar
F. W. Nijhoff, A higher-rank version of the Q3 equation, preprint (2011) , arXiv:1104.1166v2 . Google Scholar
F. W. Nijhoff , J. Atkinson and J. Hietarinta , J. Phys. A: Math. Theor. 42 , 34 ( 2009 ) . Crossref, Web of Science, Google Scholar
F. W. Nijhoff et al. , Inverse Problems 8 , 597 ( 1992 ) . Crossref, Web of Science, Google Scholar
Y. Shi and D. J. Zhang , SIGMA 7 , 11 ( 2011 ) . Google Scholar
A. Tongas and F. W. Nijhoff, Glasgow Math. J. 47(A), 205 (2005). Crossref, Web of Science, Google Scholar
A. J. Walker, Similarity reductions and integrable lattice equations, Ph. D. thesis, Leeds University (2001) . Google Scholar
D. J. Zhang, Notes on solutions in Wronskian form to soliton equations: KdV-type, preprint (2006) , arXiv:nlin.SI/0603008 . Google Scholar
D. J. Zhang and J. Hietarinta, Generalized double-Wronskian solutions to the nonlinear Schrödinger equation, preprint (2005) . Google Scholar
D. J. Zhang and J. Hietarinta, Generalized solutions for the H1 model in ABS list of lattice equations, in Nonlinear and Modern Mathematical Physics: Proc. First Int. Workshop, AIP Conference Proceedings, Vol. 1212 (Springer-Verlag GmbH, 2010), pp. 154–161 . Google Scholar
D. J. Zhang and S. L. Zhao, Solutions to the ABS lattice equations via generalized cauchy matrix approach, preprint (2012) , arXiv:1208.3752v2 . Google Scholar
D. J. Zhang , S. L. Zhao and F. W. Nijhoff , Stud. Appl. Math. 129 , 220 ( 2012 ) . Crossref, Web of Science, Google Scholar
S. L. Zhao, D. J. Zhang and Y. Shi, Chin. Ann. Math. B 33(2), 259 (2012). Crossref, Web of Science, Google Scholar