本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退...本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退化为相应的孤立波解或三角函数解。In this letter, twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant exact doubly periodic solutions of nonlinear evolution equations. As a result, with the aid of computer symbolic computation software (for example, Maple), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m→0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.展开更多
In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved ...In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.展开更多
In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sand...In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sandwich laminated shells with varying thickness are established using the modified variational principle within the framework of first-order shear deformation theory(FSDT).The displacement components of the sandwich shell are expanded using the MJPI shape function and Fourier series in the meridional and circumferential directions,respectively.The accuracy and reliability of the proposed MJPI shape function are validated against numerical results from published literature and the commercial simulation tool Abaqus.Finally,the effects of different parameters such as thickness gradient,thickness power index and boundary condition on the free vibration and dynamic response of the sandwich laminated shell are investigated.展开更多
文摘本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退化为相应的孤立波解或三角函数解。In this letter, twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant exact doubly periodic solutions of nonlinear evolution equations. As a result, with the aid of computer symbolic computation software (for example, Maple), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m→0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.
文摘In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.
文摘In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sandwich laminated shells with varying thickness are established using the modified variational principle within the framework of first-order shear deformation theory(FSDT).The displacement components of the sandwich shell are expanded using the MJPI shape function and Fourier series in the meridional and circumferential directions,respectively.The accuracy and reliability of the proposed MJPI shape function are validated against numerical results from published literature and the commercial simulation tool Abaqus.Finally,the effects of different parameters such as thickness gradient,thickness power index and boundary condition on the free vibration and dynamic response of the sandwich laminated shell are investigated.
