By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions ...By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.展开更多
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by J...Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.展开更多
Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calc...Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.展开更多
文摘By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.
基金National Natural Science Foundation of China under Grant Nos.10475055 and 90503006the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20040969
文摘Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ^4 model are presented. Simultaneously, inspired by the new solutions of the famous φ^4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scaiar field （NCSF） system are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
