A New (2+1)-Dimensional Integrable Equation
作者： Ren Bo , Lin Ji
DOI: 10.1088/0253-6102/51/1/03
关键词: Mathematics 、 Inverse scattering transform 、 Integro-differential equation 、 First-order partial differential equation 、 Partial differential equation 、 Lax pair 、 Kadomtsev–Petviashvili equation 、 Burgers' equation 、 Differential equation 、 Mathematical physics
摘要: A new nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained from the mKP by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling. In order to demonstrate integrability property equation, corresponding Lax pair applying technique equation.
harvard.edu
sci-hub.se 参考文章(17)
Shu-fang Deng, Darboux transformations for the isospectral and nonisospectral mKP equation Physica A-statistical Mechanics and Its Applications. ,vol. 382, pp. 487- 493 ,(2007) , 10.1016/J.PHYSA.2007.04.009
F. Calogero, Ji Xiaoda, C‐integrable nonlinear partial differentiation equations. I Journal of Mathematical Physics. ,vol. 32, pp. 875- 887 ,(1991) , 10.1063/1.529346
Attilio Maccari, The investigation into new integrable systems of equations in 2+1-dimensions Journal of Mathematical Physics. ,vol. 44, pp. 242- 250 ,(2003) , 10.1063/1.1525405
Attilio Maccari, On the integrability of a new Davey–Stewartson type equation in 2+1 dimensions Physics Letters A. ,vol. 265, pp. 187- 193 ,(2000) , 10.1016/S0375-9601(99)00842-7
Attilio Maccari, Nonresonant interacting waves for the nonlinear Klein—Gordon equation in three-dimensional space Physica D: Nonlinear Phenomena. ,vol. 135, pp. 331- 344 ,(2000) , 10.1016/S0167-2789(99)00142-6
Attilio Maccari, A class of integrable Davey–Stewartson type systems Journal of Mathematical Physics. ,vol. 42, pp. 2689- 2700 ,(2001) , 10.1063/1.1370396
F Calogero, W Eckhaus, Nonlinear evolution equations, rescalings, model PDEs and their integrability: II Inverse Problems. ,vol. 4, pp. 11- 33 ,(1987) , 10.1088/0266-5611/4/1/005
B.G. Konopelchenko, V.G. Dubrovsky, Some new integrable nonlinear evolution equations in 2 + 1 dimensions Physics Letters A. ,vol. 102, pp. 15- 17 ,(1984) , 10.1016/0375-9601(84)90442-0
Xianguo Geng, Yongtang Wu, Cewen Cao, Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation Journal of Physics A. ,vol. 32, pp. 3733- 3742 ,(1999) , 10.1088/0305-4470/32/20/306
F. Calogero, Ji Xiaoda, C‐integrable nonlinear PDEs. II Journal of Mathematical Physics. ,vol. 32, pp. 2703- 2717 ,(1991) , 10.1063/1.529112