CTE Solvability, Nonlocal Symmetries and Exact Solutions of Dispersive Water Wave System

CHEN Chun-Li; LOU Sen-Yue

PDF(194 KB)

Communications in Theoretical Physics ›› 2014, Vol. 61 ›› Issue (05) : 545-550.

General

CTE Solvability, Nonlocal Symmetries and Exact Solutions of Dispersive Water Wave System

Author information +

History +

Abstract

A consistent tanh expansion (CTE) method is developed for the dispersion water wave (DWW) system. For the CTE solvable DWW system, there are two branches related to tanh expansion, the main branch is consistent while the auxiliary branch is not consistent. From the consistent branch, we can obtain infinitely many exact significant solutions including the soliton-resonant solutions and soliton-periodic wave interactions. From the inconsistent branch, only one special solution can be found. The CTE related nonlocal symmetries are also proposed. The nonlocal symmetries can be localized to find finite Bäcklund transformations by prolonging the model to an enlarged one.

Key words

consistent tanh expansion / dispersion water wave (DWW) system / nonlocal symmetries / the consistent Riccati expansion

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

CHEN Chun-Li, LOU Sen-Yue. CTE Solvability, Nonlocal Symmetries and Exact Solutions of Dispersive Water Wave System[J]. Communications in Theoretical Physics, 2014, 61(05): 545-550

References

[1] C.H. Gu, H.S. Hu, and Z.X. Zhou, Darboux Transformations in Integrable Systems Theory and their Applications to Geometry, Series: Mathematical Physics Studies, Vol. 26, Springer, Dordrecht (2005).

[2] S.Y. Lou and X.B. Hu, J. Math. Phys. 38 (1997) 6401; S.Y. Lou and X.B. Hu, J. Phys. A 30 (1997) L95.

[3] X.R. Hu, S.Y. Lou, and Y. Chen, Phys. Rev. E 85 (2012) 056607.

[4] C. Rogers and W.K. Schief, Bäcklund and Darboux Transformations, Geometry and Modern Applications in Soliton Theory, Cambridge University Press, Cambridge (2002).

[5] S.Y. Lou, X.R. Hu, and Y. Chen, J. Phys. A: Math. Theor. 45 (2012) 155209.

[6] X.N. Gao, S.Y. Lou, and X.Y. Tang, J. High Energy Phys. 05 (2013) 029.

[7] S.Y. Lou, Residual Symmetries and Bäcklund Transformations, arXiv:1308.1140 (2013).

[8] D.J. Korteweg and F. de Vries, Philos. Mag. 39 (1895) 422; D.G. Crighton, Acta Appl. Math. 39 (1995) 39.

[9] S.Y. Lou, J. Math. Phys. 35 (1994) 2390; S.Y. Lou and X.B. Hu, Chin. Phys. Lett. 10 (1993) 577.

[10] D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, and C. Tang, Rev. Mod. Phys. 58 (1986) 4; J. Weiss, J. Math. Phys. 24 (1986) 1293.

[11] S.Y. Lou, Physica Scripta 54 (1996) 428.

[12] B.B. Kadomtsev and V.I. Petviashvili, Dokl. Akad. Nauk SSSR 192 (1970) 753.

[13] X.P. Cheng, C.L. Chen, and S.Y. Lou, Interactions Among Different Types of Nonlinear Waves Described by the Kadomtsev-Petviashvili Equation, arXiv:1208.3259.

[14] K. Sawada and T. Kotera, Progr. Theor. Phys. 51 (1974) 1355; P.J. Caudrey, R.K. Dodd, and J.D. Gibbon, Proc. Roy. Soc. London A 351 (1976) 407.

[15] S.Y. Lou, Phys. Lett. A 175 (1993) 23; S.Y. Lou, H.Y. Ruan, W.Z. Chen, Z.L. Wang, and L.L. Chen, Chin. Phys. Lett. 11 (1994) 593.

[16] Y. Jin, M. Jia, and S.Y. Lou, Commun. Theor. Phys. 58 (2012) 795; Y. Jin, M. Jia, and S.Y. Lou, Chin. Phys. Lett. 30 (2013) 020203; S.P. Pudasaini, Phys. Fluid. 23 (2011) 043301.

[17] Y.S. Kivshar and B.A. Malomed, Rev. Mod. Phys. 61 (1989) 763; Yu S. Kivshar and B. Luther-Davies, Phys. Rep. 298 (1998) 81.

[18] S.Y. Lou, X.P. Cheng, C.L. Chen, and X.Y. Tang, Interactions Between Solitons and Other Nonlinear Schrödinger Waves, arXiv:1208.5314.

[19] S.Y. Lou, Consistent Riccati Expansion and Solvability, arxiv:1308.5891.

[20] B.H. Kupershmidt, Commun. Math. Phys. 99 (1985) 51.

[21] S.Y. Lou and X.B. Hu, J. Math. Phys. 38 (1997) 6401.

[22] H.B. Lan and K.L. Wang, J. Phys. A: Math. Gen. 23 (1990) 3923; S.Y. Lou, G.X. Huang, and H.Y. Ruan, J. Phys. A: Math. Gen. 24 (1991) L587; E.J. Parkes and B.R. Duffy, Comp. Phys. Commun. 98 (1996) 288; E.G. Fan, Phys. Lett. A 277 (2000) 212.

[23] V.V. Gudkov, J. Math. Phys. 38 (1997) 4794; P.J. Olver, J. Math. Phys. 18 (1977) 1212.

[24] S. Wang, X.Y. Tang, and S.Y. Lou, Chaos, Solitons & Fractals 21 (2003) 231.

Funding

Supported by the National Natural Science Foundations of China under Grant Nos. 11175092, 11275123, 11205092, and 10905038, Talent Fund and K. C. Wong Magna Fund in Ningbo University