Some new exact solutions of the Burgers--Fisher equation and
generalized Burgers--Fisher equation have been obtained by using the
first integral method. These solutions include exponential function
solutions, singular solitary wave solutions and some more complex
solutions whose figures are given in the article. The result shows
that the first integral method is one of the most effective
approaches to obtain the solutions of the nonlinear partial
differential equations. 相似文献
Shielding effects of the surrounding arms and chains on the reactive centers taking part in RAFT four‐arm star polymerization following the Z‐group approach are calculated by means of exact enumeration of star/chain samples prepared by Monte Carlo techniques. The shielding effect, which can be relieved when using expanded core moieties, increases with increasing chain (arm) lengths. This leads to a reduction of the contact probability according to a power law with an exponent of −0.4 to −0.45. Additionally, characteristic chain properties and shape parameters are calculated as a function of the distance between the center of the star and the end of the linear chain in order to gain deeper insight into the mechanism of contact formation preceding the actual reaction.
Explicit exact solution of supersymmetric Toda fields associated
with the Lie superalgebra sl(2|1) is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral
Drienfeld-Sokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp(1|2). The problem lies
in that a key step in the construction makes use of the tensor
product decomposition of the highest weight representations of the
underlying Lie superalgebra, which is not clear until recently. So
our construction made in this paper presents a first explicit
example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1. 相似文献
Nonlinear dispersive generalized Benjiamin–Bona–Mahony equations are studied by using a generalized algebraic method. New
abundant families of explicit and exact traveling wave solutions, including triangular periodic, solitary wave, periodic-like,
soliton-like, rational and exponential solutions are constructed, which are in agreement with the results reported in other
literatures, and some new results are obtained. These solutions will be helpful to the further study of the physical meaning
and laws of motion of the nature and the realistic models. The proposed method in this paper can be further extended to the
2+1 dimensional and higher dimensional nonlinear evolution equations or systems of equations. 相似文献
New state space formulations for the free vibration of circular, annular and sectorial plates are established by introducing
two displacement functions and two stress functions. The state variables can be separated into two independent catalogues
and two kinds of vibrations can be readily found. Expanding the displacements and stresses in terms of Bessel functions in
the radial direction and trigonometric functions in the circumferential direction, we obtained the exact frequency equation
for the free vibration for some uncommon boundary conditions. Numerical results are presented and compared with those of FEM
to demonstrate the reliability of the proposed method. A parametric investigation is also performed. 相似文献
By truncating the Painlevé expansion at the constant level term, the Hirota bilinear form is obtained for a (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation. Based on its bilinear form, solitary-wave solutions are constructed via the ε-expansion method and the corresponding graphical analysis is given. Furthermore, the exact solution in the Wronskianform is presented and proved by direct substitution into the bilinear equation. 相似文献
The generalized conditional symmetry method, which is a generalization of the conditional symmetry method, is used to study the nonlinear diffusion-convection-reaction equations. In particular, power law and exponential diffusivities are examined and we derive mathematical forms of the convection and reaction terms which permit a new type of generalized conditional symmetry. Some new exact solutions of the governing equations can be obtained by solving the systems of two or three ordinary differential equations which arise from the compatibility of the generalized conditional symmetries and the governing equations. 相似文献
Lie point symmetries associated with the new (2 l)-dimensional KdV equation ut 3uxuy uxxy = 0 are investigated. Some similarity reductions are derived by solving the the soliton solution is obtained directly from the B(a)cklund transformation. 相似文献