×

Exact homoclinic wave and soliton solutions for the 2D Ginzburg-Landau equation. (English) Zbl 1220.35168

Summary: New exact wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D Ginzburg-Landau equation are obtained using the auxiliary function method, generalized Hirota method and the ansatz function technique under the certain constraint conditions of coefficients in equation, respectively. The result shows that there exists a kink-wave solution which tends to one and the same periodic wave solution as time tends to infinite.

MSC:

35Q56 Ginzburg-Landau equations
35Q51 Soliton equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Temam, R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics (2001), Springer-Verlag
[2] Blennerhassett, P. J., Philos. Trans. R. Soc. London, Ser. A, 298, 451 (1980)
[3] Moon, H. T.; Huerre, P.; Redekopp, L. G., Phys. Rev. Lett., 49, 485 (1982)
[4] Moon, H. T.; Huerre, P.; Redekopp, L. G., Physica D, 7, 135 (1983)
[5] Fang, F.; Xiao, Y., Opt. Commun., 268, 2, 305 (2006)
[6] Abdul-Majida; Wazwaz, Appl. Math. Lett., 19, 10, 1007 (2006)
[7] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution and Inverse Scattering (1991), Cambridge Univ. Press · Zbl 0762.35001
[8] Dai, Z.; Li, S.; Li, D.; Zhu, A., Chaos Solitons Fractals, 34, 4, 1148 (2007)
[9] van Saarloos, W.; Hohenberg, P. C., Physica D, 56, 303 (1992)
[10] Akhmediev, N.; Ankiewicz, A., Solitons. Nonlinear Pulses and Beams (1997), Chapman and Hall: Chapman and Hall London · Zbl 1218.35183
[11] Zhou, Y. B.; Wang, M. L., Phys. Lett. A, 308, 31 (2003)
[12] Zhou, Y.; Wang, M.; Miao, T., Phys. Lett. A, 323, 77 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.