This page has only limited features, please log in for full access.
May 2019
North China Electric Power University
Apr. 2019
Consortium for Mathematics and Its Application of the United States
Mr. Weiqin Chen obtained a B.E. degree from School of Energy Power and Mechanical Engineering at North China Electric Power University in June 2020. From 2021 fall, he will pursue a Ph.D. degree in Rensselaer Polytechnic Institute in U.S.
Project Goal: Investigating the nonautonomous motions of high dimensional lump solutions under physical modulations
Current Stage: Paper published
Project Goal: Studying the characteristics of the lump waves of (2+1)-dimensional KdV equations with variable coefficients
Current Stage: Paper published
Under investigation in this paper is a (3 + 1)-dimensional variable-coefficient generalized shallow water wave equation. The exact lump solutions of this equation are presented by virtue of its bilinear form and symbolic computation. Compared with the solutions of the previous cases, these solutions contain two inhomogeneous coefficients, which can show some interesting nonautonomous characteristics. Three types of dispersion coefficients are considered, including the periodic, exponential, and linear modulations. The corresponding nonautonomous lump waves have different characteristics of trajectories and velocities. The periodic fission and fusion interaction between a lump wave and a kink soliton is discussed graphically.
Wei-Qin Chen; Qing-Feng Guan; Chao-Fan Jiang; Fei-Fan Zhang; Lei Wang; Weiqin Chen. Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)-Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients. Complexity 2019, 2019, 1 -8.
AMA StyleWei-Qin Chen, Qing-Feng Guan, Chao-Fan Jiang, Fei-Fan Zhang, Lei Wang, Weiqin Chen. Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)-Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients. Complexity. 2019; 2019 ():1-8.
Chicago/Turabian StyleWei-Qin Chen; Qing-Feng Guan; Chao-Fan Jiang; Fei-Fan Zhang; Lei Wang; Weiqin Chen. 2019. "Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)-Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients." Complexity 2019, no. : 1-8.
We study a (2+1)-dimensional Korteweg–de Vries (KdV) equation with variable coefficients. By virtue of Hirota method, we present three types of nonautonomous lump solutions including the bright, bright-dark and dark lump ones. By considering different types of dispersion coefficients, we investigate the characteristics of trajectories, velocities and displacements of nonautonomous bright lump wave, which are different from the case of its constant-coefficient counterpart. We finally demonstrate the periodic attraction and repulsion interaction between a lump wave and a soliton. Our results might provide some physical insights into the relevant fields in nonlinear science.
Fei-Peng Chen; Wei-Qin Chen; Lei Wang; Zhen-Jun Ye. Nonautonomous characteristics of lump solutions for a (2+1)-dimensional Korteweg–de Vries equation with variable coefficients. Applied Mathematics Letters 2019, 96, 33 -39.
AMA StyleFei-Peng Chen, Wei-Qin Chen, Lei Wang, Zhen-Jun Ye. Nonautonomous characteristics of lump solutions for a (2+1)-dimensional Korteweg–de Vries equation with variable coefficients. Applied Mathematics Letters. 2019; 96 ():33-39.
Chicago/Turabian StyleFei-Peng Chen; Wei-Qin Chen; Lei Wang; Zhen-Jun Ye. 2019. "Nonautonomous characteristics of lump solutions for a (2+1)-dimensional Korteweg–de Vries equation with variable coefficients." Applied Mathematics Letters 96, no. : 33-39.