The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
In this paper, a new special ansatz solution, where elliptic equation satisfied by elliptic functions is fallen as an intermediate transformation, is applied to solve the KdV-Burgers-Kuramoto equation, and many morene...In this paper, a new special ansatz solution, where elliptic equation satisfied by elliptic functions is fallen as an intermediate transformation, is applied to solve the KdV-Burgers-Kuramoto equation, and many morenew periodic solutions are obtadned, including solutions expressed in terms of Jacobi elliptic functions, solution expressed in terms of Weierstrass elliptic function.展开更多
This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weie...This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.展开更多
This paper presents an elastic solution to the pressure-controlled elliptical cavity expansion problem under the anisotropic stress conditions. The problem is formulated by the assumption that an initial elliptical ca...This paper presents an elastic solution to the pressure-controlled elliptical cavity expansion problem under the anisotropic stress conditions. The problem is formulated by the assumption that an initial elliptical cavity is expanded under a uniform pressure and subjected to an in-plane initial horizontal pressure Kσ_0 and vertical pressure σ_0 at infinity. A conformal mapping technique is used to map the outer region of the initial elliptical cavity in the physical plane onto the inner region of a unit circle in the phase plane. Using the complex variable theory, the stress functions are derived; hence, the stress and displacement distributions around the elliptical cavity wall can be obtained. Furthermore, a closed-form solution to the pressure-expansion relationship is presented based on the elastic solution to the stress and displacement. Next, the proposed analytical solutions are validated by comparing with the Kirsch's solution and the finite element method(FEM). The solution to the presented pressure-controlled elliptical cavity expansion can be applied to two cases in practice. One is to employ the solution to the interpretation of the shear modulus of the soil or rocks and the in-situ stress in the pre-bored pressuremeter test under the lateral anisotropic initial stress condition. The other is the interpretation of the membrane expansion of a flat dilatometer test using the pressure-controlled elliptical cavity expansion solution. The two cases in practice confirm the usefulness of the present analytical solution.展开更多
文摘The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
基金The project supported by National Natural Science Foundation of China under Grant No. 40305006
文摘In this paper, a new special ansatz solution, where elliptic equation satisfied by elliptic functions is fallen as an intermediate transformation, is applied to solve the KdV-Burgers-Kuramoto equation, and many morenew periodic solutions are obtadned, including solutions expressed in terms of Jacobi elliptic functions, solution expressed in terms of Weierstrass elliptic function.
基金supported by the Open Project of Key Laboratory of Mathematics Mechanization,CAS under Grant No.KLMM0602
文摘This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation.Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.
基金supported by the National Natural Science Foundation of China(Grant No.51278170)the National Science Joint High Speed Railway Foundation of China(Grant No.U1134207)+1 种基金the"111"Project(Grant No.B13024)the Fundamental Research Funds for the Central Universities(Grant No.2014B02814)
文摘This paper presents an elastic solution to the pressure-controlled elliptical cavity expansion problem under the anisotropic stress conditions. The problem is formulated by the assumption that an initial elliptical cavity is expanded under a uniform pressure and subjected to an in-plane initial horizontal pressure Kσ_0 and vertical pressure σ_0 at infinity. A conformal mapping technique is used to map the outer region of the initial elliptical cavity in the physical plane onto the inner region of a unit circle in the phase plane. Using the complex variable theory, the stress functions are derived; hence, the stress and displacement distributions around the elliptical cavity wall can be obtained. Furthermore, a closed-form solution to the pressure-expansion relationship is presented based on the elastic solution to the stress and displacement. Next, the proposed analytical solutions are validated by comparing with the Kirsch's solution and the finite element method(FEM). The solution to the presented pressure-controlled elliptical cavity expansion can be applied to two cases in practice. One is to employ the solution to the interpretation of the shear modulus of the soil or rocks and the in-situ stress in the pre-bored pressuremeter test under the lateral anisotropic initial stress condition. The other is the interpretation of the membrane expansion of a flat dilatometer test using the pressure-controlled elliptical cavity expansion solution. The two cases in practice confirm the usefulness of the present analytical solution.
