Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solut...Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.展开更多
The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trig...The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort.展开更多
In terms of the solutions of the generalized Riccati equation,a new algebraic method,which contains theterms of radical expression of functions f(ξ),is constructed to explore the new exact solutions for nonlinear evo...In terms of the solutions of the generalized Riccati equation,a new algebraic method,which contains theterms of radical expression of functions f(ξ),is constructed to explore the new exact solutions for nonlinear evolutionequations.Being concise and straightforward,the method is applied to nonlinear Klein Gordon equation,and some newexact solutions of the system are obtained.The method is of important significance in exploring exact solutions for othernonlinear evolution equations.展开更多
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational funct...This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11502123 and11262012)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2015JQ01)
文摘Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort.
基金the Science and Technology Foundation of Guizhou Province of China under Grant No.20072009
文摘In terms of the solutions of the generalized Riccati equation,a new algebraic method,which contains theterms of radical expression of functions f(ξ),is constructed to explore the new exact solutions for nonlinear evolutionequations.Being concise and straightforward,the method is applied to nonlinear Klein Gordon equation,and some newexact solutions of the system are obtained.The method is of important significance in exploring exact solutions for othernonlinear evolution equations.
基金Project supported by the Fundamental Research Funds for the Central Universities （Grant No. 2010B17914） and the National Natural Science Foundation of China （Grant No. 10926162）.
文摘This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.
