Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids

Pramana

Kun Su1¹  Yan Jiang1¹  Bo Tian1 2¹  Pan Wang1¹ 

[1] State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China$$

关键词: Infinitely-many conservation laws;    (2+1)-dimensional nonlinear evolution equations;    Kadomtsev–Petviashvili equation;    Davey–Stewartson equation;    Lax pair;    symbolic computation.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.

【 授权许可】

Unknown