We shall study the differential equation y^l2=Tn（y）-（1-2μ2）;where μ2 is a constant, Tn（x） are the Chebyshev polynomials with n = 3,4,6. The solutions of the differential equations will be expressed explicitly...We shall study the differential equation y^l2=Tn（y）-（1-2μ2）;where μ2 is a constant, Tn（x） are the Chebyshev polynomials with n = 3,4,6. The solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on 2F1 （1/4, 3/4; 1; z）, 2F1 （l/3, 2/3; 1; z）, 2F1 （1/6, 5/6; 1; z） and provide a unified approach to a set of identities of Rmanujan involving these hypergeometric functions.展开更多
In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik...In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.展开更多
文摘We shall study the differential equation y^l2=Tn（y）-（1-2μ2）;where μ2 is a constant, Tn（x） are the Chebyshev polynomials with n = 3,4,6. The solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on 2F1 （1/4, 3/4; 1; z）, 2F1 （l/3, 2/3; 1; z）, 2F1 （1/6, 5/6; 1; z） and provide a unified approach to a set of identities of Rmanujan involving these hypergeometric functions.
基金The Scientific Research Foundation (QKJA2010011) of Nanjing Institute of Technology
文摘In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.
