In this paper, a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota’s bilinear form and symbolic computation, lump and interaction so...In this paper, a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota’s bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained,which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution, interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented. Their interactions are shown in some 3D plots.展开更多
We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate ar...We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.展开更多
In this paper,the(3+1)-dimensional nonlinear evolution equation is studied analytically.The bilinear form of given model is achieved by using the Hirota bilinear method.As a result,the lump waves and col-lisions betwe...In this paper,the(3+1)-dimensional nonlinear evolution equation is studied analytically.The bilinear form of given model is achieved by using the Hirota bilinear method.As a result,the lump waves and col-lisions between lumps and periodic waves,the collision among lump wave and single,double-kink soliton solutions as well as the collision between lump,periodic,and single,double-kink soliton solutions for the given model are constructed.Furthermore,some new traveling wave solutions are developed by applying the exp(−φ(ξ))expansion method.The 3D,2D and contours plots are drawn to demonstrate the nature of the nonlinear model for setting appropriate set of parameters.As a result,a collection of bright,dark,periodic,rational function and elliptic function solutions are established.The applied strategies appear to be more powerful and efficient approaches to construct some new traveling wave structures for various contemporary models of recent era.展开更多
This paper extends a method, called bilinear neural network method(BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test funct...This paper extends a method, called bilinear neural network method(BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model,specific activation functions of "2-2" model and arbitrary functions of "2-2-3" model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gB KP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots,the evolution characteristic of these waves are exhibited.展开更多
基金Project supported by National Natural Science Foundation of China(Grant No 81960715)Science and Technology Project of Education Department of Jiangxi Province(GJJ151079)。
文摘In this paper, a generalized (3+1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota’s bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained,which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution, interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented. Their interactions are shown in some 3D plots.
文摘We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.
文摘In this paper,the(3+1)-dimensional nonlinear evolution equation is studied analytically.The bilinear form of given model is achieved by using the Hirota bilinear method.As a result,the lump waves and col-lisions between lumps and periodic waves,the collision among lump wave and single,double-kink soliton solutions as well as the collision between lump,periodic,and single,double-kink soliton solutions for the given model are constructed.Furthermore,some new traveling wave solutions are developed by applying the exp(−φ(ξ))expansion method.The 3D,2D and contours plots are drawn to demonstrate the nature of the nonlinear model for setting appropriate set of parameters.As a result,a collection of bright,dark,periodic,rational function and elliptic function solutions are established.The applied strategies appear to be more powerful and efficient approaches to construct some new traveling wave structures for various contemporary models of recent era.
基金supported by the National Natural Science Foundation of China under Grant Nos.11661060,11571008the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT-20-A06the Natural Science Foundation of Inner Mongolia Autonomous Region of China under Grant No.2018LH01013。
文摘This paper extends a method, called bilinear neural network method(BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model,specific activation functions of "2-2" model and arbitrary functions of "2-2-3" model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gB KP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots,the evolution characteristic of these waves are exhibited.
