In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation ...In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.展开更多
In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function ...In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.展开更多
本文根据三波法的思想,结合一类新的KdV方程的Hirota双线性形式,通过选择特定形式的试探函数,构造出该方程的孤波解与周期解,并对解中的参数赋值,利用计算机符号软件对部分解进行了数值模拟,观察解的三维波形图与动力学演化过程。In thi...本文根据三波法的思想,结合一类新的KdV方程的Hirota双线性形式,通过选择特定形式的试探函数,构造出该方程的孤波解与周期解,并对解中的参数赋值,利用计算机符号软件对部分解进行了数值模拟,观察解的三维波形图与动力学演化过程。In this paper, based on the idea of the three-wave method, combined with a new class of Hirota bilinear forms of the KdV equation, we constructed the solitary-wave solution and the periodic solution of the equation by choosing a specific form of the trial function and assigning values to the parameters in the solution, and numerically simulated some of the solutions by using the computer symbolic software, observing the three-dimensional waveform plots of the solutions with the dynamics evolution process.展开更多
基金Supported by the Jiangsu Higher School Undergraduate Innovation and Entrepreneurship Training Program(202311117078Y)。
文摘In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.
文摘In this paper,the exact boundary controllability of the higher-order KdVtype equation on torus is studied.That is,given the initial and final states in the appropriate space,by adding the appropriate control function on the boundary,the solution of the system can transition from the initial state to the specified final value.Firstly,we establish the observability inequality for the higher-order KdV-type equation by Ingham inequality.Then,based on the observability inequality,Hilbert uniqueness method and a integral identity we obtain the exact boundary controllability of the higher-order KdV-type equation.
文摘本文根据三波法的思想,结合一类新的KdV方程的Hirota双线性形式,通过选择特定形式的试探函数,构造出该方程的孤波解与周期解,并对解中的参数赋值,利用计算机符号软件对部分解进行了数值模拟,观察解的三维波形图与动力学演化过程。In this paper, based on the idea of the three-wave method, combined with a new class of Hirota bilinear forms of the KdV equation, we constructed the solitary-wave solution and the periodic solution of the equation by choosing a specific form of the trial function and assigning values to the parameters in the solution, and numerically simulated some of the solutions by using the computer symbolic software, observing the three-dimensional waveform plots of the solutions with the dynamics evolution process.
