In this paper,we primarily investigate several exact solutions of the(2+1)-dimensional KdV equation and summarize the trajectory equations after collisions between these solutions.Using the bilinear form with specific...In this paper,we primarily investigate several exact solutions of the(2+1)-dimensional KdV equation and summarize the trajectory equations after collisions between these solutions.Using the bilinear form with specific test functions and the parameter limiting technique,we construct T-order breather solutions,L-order lump solutions,and hybrid solutions.On this basis,we examine the close relationship between the positions of breather solutions and the parameters,the motion trajectories resulting from the interaction of lump solutions,as well as the trajectories of a single lump before and after its collision with higher-order soliton solutions.展开更多
The study derives the Hirota bilinear form for a variable-coefficient(2+1)-dimensional BKP equation and constructs N-soliton,M-lump,and mixed lumpsoliton solutions.By testing four representative time-dependent coeffic...The study derives the Hirota bilinear form for a variable-coefficient(2+1)-dimensional BKP equation and constructs N-soliton,M-lump,and mixed lumpsoliton solutions.By testing four representative time-dependent coefficient sets,the authors visualise howα(t),β(t)andδ(t)shape the spatial patterns of solitons and lumps.The work emphasises the richer structural diversity and evolution pathways that arise when coefficients vary with time.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12461047)the Scientific Research Project of the Hunan Education Department(Grant No.24B0478).
文摘In this paper,we primarily investigate several exact solutions of the(2+1)-dimensional KdV equation and summarize the trajectory equations after collisions between these solutions.Using the bilinear form with specific test functions and the parameter limiting technique,we construct T-order breather solutions,L-order lump solutions,and hybrid solutions.On this basis,we examine the close relationship between the positions of breather solutions and the parameters,the motion trajectories resulting from the interaction of lump solutions,as well as the trajectories of a single lump before and after its collision with higher-order soliton solutions.
基金supported by the National Natural Science Foundation of China(Grant No.12461047)the Scientific Research Project of the Hunan Education Department(Grant No.24B0478).
文摘The study derives the Hirota bilinear form for a variable-coefficient(2+1)-dimensional BKP equation and constructs N-soliton,M-lump,and mixed lumpsoliton solutions.By testing four representative time-dependent coefficient sets,the authors visualise howα(t),β(t)andδ(t)shape the spatial patterns of solitons and lumps.The work emphasises the richer structural diversity and evolution pathways that arise when coefficients vary with time.
