Wei, Cai-Min; Wang, Jian-Jun Travelling wave solutions to the generalized stochastic KdV equation. (English) Zbl 1148.35349 Chaos Solitons Fractals 37, No. 3, 733-740 (2008). Summary: By Hermite transformation and a general mapping deformation method, a generalized stochastic KdV equation is considered. Many new types of travelling wave solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained. Cited in 2 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 35C05 Solutions to PDEs in closed form 35B10 Periodic solutions to PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:stochastic KdV equation; Hermite transform; travelling wave solutions; solitary wave solutions; periodic wave solutions PDFBibTeX XMLCite \textit{C.-M. Wei} and \textit{J.-J. Wang}, Chaos Solitons Fractals 37, No. 3, 733--740 (2008; Zbl 1148.35349) Full Text: DOI References: [1] Lou, S. Y.; Ni, G. J., J Math Phys, 30, 1614 (1989) [2] Li, H. M., Chin Phys Lett, 19, 745 (2002) [3] Fan, E. G., Phys Lett A, 277, 212 (2000) [4] Fan, E. G., Chaos, Solitons & Fractals, 16, 819 (2003) [5] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Acta Phys Sin, 50, 2068 (2001) [6] Yan, Z. Y.; Zhang, H. Q., Acta Phys Sin, 48, 1957 (1999) [7] Zhang, J. L.; Wang, Y. M.; Wang, M. L.; Fang, Z. D., Acta Phys Sin, 52, 1578 (2003) [8] Zhang, J. F.; Chen, F. Y., Acta Phys Sin, 50, 1648 (2001) [9] Li, D. S.; Zhang, H. Q., Acta Phys Sin, 52, 1573 (2003) [10] Wadati, M., J Phys Soc Jpn, 52, 2642 (1983) [11] Wadati, M.; Akutsu, Y., J Phys Soc Jpn, 53, 3342 (1984) [12] Wadati, M., J Phys Soc Jpn, 59, 4201 (1990) [13] de Bouard, A.; Debussche, A., J Funct Anal, 154, 215 (1998) [14] de Bouard, A.; Debussche, A., J Funct Anal, 169, 532 (1999) [15] Debussche, A.; Printems, J., Physica D, 134, 200 (1999) [16] Debussche, A.; Printems, J., J Comput Anal Appl, 3, 3, 183 (2001) [17] Konotop, V. V.; Vzquez, L., Nonlinear random waves (1994), World Scientific [18] Printems, J., J Differen Equat, 153, 338 (1999) [19] Xie, Y. C., Phys Lett A, 310, 161 (2003) [20] Xie, Y. C., Chaos, Solitons & Fractals, 20, 337 (2004) [21] Wei, C. M.; Xia, Z. Q.; Tian, N. S., Chaos, Solitons & Fractals, 26, 1, 551 (2005) [22] Wei, C. M.; Xia, Z. Q.; Tian, N. S., Acta Phys Sin, 54, 6, 2463 (2005) [23] Holden, H.; Øsendal, B.; Ubøe, J.; Zhang, T., Stochastic partial differential equations (1996), Birhkäuser [24] Guo, G. P.; Zhang, J. F., Acta Phys Sin, 51, 1159 (2002) [25] Yao, R. X.; Li, Z. B., Chin Phys, 11, 864 (2002) [26] Wang, M. L.; Zhang, J. L.; Wang, Y. M., Chin Phys, 12, 1341 (2003) [27] Guo, G. P.; Wang, R. M.; Zhang, J. F., Acta Phys Sin, 52, 2660 (2003) [28] Zhu, J. M.; Zheng, C. L.; Ma, Z. Y., Chin Phys, 13, 12, 2008 (2004) [29] Benth, E.; Gjerde, J., Potential Anal, 8, 2, 179 (1998) 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.