A three-wave interaction model with self-consistent sources: The ∂¯-dressing method and solutions

作者: Yonghui Kuang , Junyi Zhu

DOI: 10.1016/J.JMAA.2015.01.072

关键词:

摘要: … In this paper, we propose the three-wave interaction model with self-consistent sources (TWIM-… This system may reduce to the classical three-wave interaction model as ω ( k ) = 0 . The …

参考文章(41)
D. J. Kaup, The Three-Wave Interaction-A Nondispersive Phenomenon Studies in Applied Mathematics. ,vol. 55, pp. 9- 44 ,(1976) , 10.1002/SAPM19765519
Zeng Yun-Bo, Shao Yi-Jun, Ma Wen-Xiu, Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources Communications in Theoretical Physics. ,vol. 38, pp. 641- 644 ,(2002) , 10.1088/0253-6102/38/6/641
S Novikov, Sergei V Manakov, Lev Petrovich Pitaevskii, Vladimir Evgenevič Zakharov, Theory of Solitons: The Inverse Scattering Method ,(1984)
A. S. Fokas, V. E. Zakharov, The dressing method and nonlocal Riemann-Hilbert problems Journal of Nonlinear Science. ,vol. 2, pp. 109- 134 ,(1992) , 10.1007/BF02429853
V. K. Mel'nikov, Integrable and nonintegrable cases of the Lax equations with a source Theoretical and Mathematical Physics. ,vol. 99, pp. 733- 737 ,(1994) , 10.1007/BF01017060
Wen-Xiu Ma, Binary Bargmann symmetry constraints of soliton equations Nonlinear Analysis-theory Methods & Applications. ,vol. 47, pp. 5199- 5211 ,(2001) , 10.1016/S0362-546X(01)00629-0
Antonio Degasperis, Sara Lombardo, Exact solutions of the 3-wave resonant interaction equation Physica D: Nonlinear Phenomena. ,vol. 214, pp. 157- 168 ,(2006) , 10.1016/J.PHYSD.2006.01.003
R Beals, R R Coifman, Linear spectral problems, non-linear equations and the δ-method Inverse Problems. ,vol. 5, pp. 87- 130 ,(1989) , 10.1088/0266-5611/5/2/002
Junyi Zhu, Xianguo Geng, A hierarchy of coupled evolution equations with self-consistent sources and the dressing method Journal of Physics A: Mathematical and Theoretical. ,vol. 46, pp. 035204- ,(2013) , 10.1088/1751-8113/46/3/035204