We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to th...We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.展开更多
In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear m...In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear model.This model might be applied to describe the evolution of nonlinear waves in the ocean.Under the effect of a novel combination of nonlinearity and dispersion terms,two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form.Moreover,the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions.The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions.Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation.The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Grant No.2018RC031)the National Natural Science Foundation of China(Grant No.71971015)+1 种基金the Program of the Co-Construction with Beijing Municipal Commission of Education of China(Grant Nos.B19H100010and B18H100040)the Open Fund of IPOC(BUPT)。
文摘We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.
基金supported by the Project of the Fundamental Research Funds for the Central Universities of China(2022JBMC034)the National Natural Science Foundation of China under Grant No.12275017Beijing Laboratory of National Economic Security Early-warning Engineering,Beijing Jiaotong University
文摘In this paper,we propose a combined form of the bilinear Kadomtsev-Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation,which is linked with a novel(2+1)-dimensional nonlinear model.This model might be applied to describe the evolution of nonlinear waves in the ocean.Under the effect of a novel combination of nonlinearity and dispersion terms,two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic function solutions to the bilinear form.Moreover,the one-lump-multi-stripe solutions are constructed by the test function combining quadratic functions and multiple exponential functions.The one-lump-multi-soliton solutions are derived by the test function combining quadratic functions and multiple hyperbolic cosine functions.Dynamic behaviors of the lump solutions and mixed solutions are analyzed via numerical simulation.The result is of importance to provide efficient expressions to model nonlinear waves and explain some interaction mechanism of nonlinear waves in physics.
