an:06141791
Zbl 1270.37046
Li, Min; Xiao, Jing-Hua; Yan, Tian-Zhong; Tian, Bo
Integrability and soliton interaction of a resonant nonlinear Schr??dinger equation via binary Bell polynomials
EN
Nonlinear Anal., Real World Appl. 14, No. 3, 1669-1679 (2013).
00314105
2013
j
37K10 37K35 35C08 35Q55 11B73 33C47
resonant nonlinear Schr??dinger equation; integrability; resonant interactions; binary Bell polynomials
Summary: Under investigation in this paper is a resonant nonlinear Schr??dinger equation for the response of a hypothetical resonance medium to an action of a quasimonochromatic wave or the propagation of one-dimensional long magnetoacoustic waves in a cold collisionless plasma subject to a transverse magnetic field. Binary Bell polynomials are employed to derive the bilinear form, B??cklund transformation (BT) and Lax pair in the \(3\times 3\) matrix form. Two sets of the binary Bell polynomials are considered. Infinite conservation laws are also constructed from the BT in the binary-Bell-polynomial form. Moreover, two-soliton solutions are obtained through the Hirota method. Finally, the regular, intermediate-state and resonant soliton interactions are analyzed under certain conditions.