Integrability and Exact Solutions of the(2+1)-dimensional KdV Equation with Bell Polynomials Approach

作     者：Jun-cai PU Yong CHEN Jun-cai PU;Yong CHEN

作者机构：School of Mathematical SciencesShanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdao 266590China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2022年第38卷第4期

页      面：861-881页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.12175069 and No.12235007) Science and Technology Commission of Shanghai Municipality(No.21JC1402500 and No.22DZ2229014)。 

主　　题：the bilinear formalism bilinear B?cklund transformations Lax pair lump solution periodic wave solution the asymptotic properties 

摘      要：In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from the bilinear form.Especially,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion formula.With the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method.Moreover,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.