Some solitary wave solutions for a class of nonlinear wave equationu tt -a 1u xx +a 2u t+a 3u+a 4u 3=0are obtained by the usual formally variable separation approach and homogeneous balance method,where some new exact analytical solutions of the equation are also given.
用形式变量分离方法并结合齐次平衡思想得到一类广泛的非线性波动方程utt -a1uxx +a2 ut+a3 u +a4 u3 =0的若干孤波解 ,给出了一些新的精确解析解 .
Subsequently, the proposed anti-aliasing filter and interpolated Mth-band filter are applied to the image size alteration and a new approach to rational image scaling called separating variable method is provided.
Based on theBoltsmen's superposition and Schapery's nonlinear viscoelastic theory, the paper put forward a separating variable viscoelastic constitutive relation. From Kachanov's"continuum" concept, the damage islead to the constitutive equation. The experiment is conducted on close plied glass fiber cloth/epoxycomposite with different loading and unloading speeds and directions.
Starting from an extended mapping approach and a linear variable separation method, new families of exact solutions with arbitrary functions for (2+1)-dimensional Generalized Nozhnik-Nivikov-Veselov system(GNNV) are derived.
This paper is about some skills of typical questions proving and analyzing four basic methods that how to use Differential Medial Theorem:Direct method,Original Function method,Constant Inactive method and Variable Separation method.
The first one is to expand the nonlinear systems according to multi_arbitrary functions, the second one is to expand the variable separation ansatz. The third one is the MLVSA based on the Darboux transformation (DT_MLVSA) and the last one is the derivative_dependent functional variable separation method.
Another proof of Joseph and Letzter's separation of variables theorem for quantum groups
Originally introduced in the context of separation of variables for certain partial differential equations, PSWFs became an important tool for the analysis of band-limited functions after the famous series of articles by Slepian et al.
Our implementation is based on the "Separation of Variables" technique (see, e.g., Maslen and Rockmore, Proceedings of the DIMACS Workshop on Groups and Computation, pp.
Further analysis involves a separation of variables and considers a finite size of a central body.
The L-matrix is selected in such a manner that in regular coordinates the separation of variables takes place.
The dual differential equation is solved by a method of separation of variable.
Separation of variable numbers of terminal myelin loops from the underlying axolemma results in the formation of bracelets of Nageotte, whereas the transverse bands of these loops disappear.
Separation of variable techniques can be applied to elliptic equations, such as Navier's equation of equilibrium for a homogeneous medium, in plane regions provided that each boundary segment defines an eigenvalue problem.
More specifically, the region can be triangulated into "convex" elements and separation of variable methods used to generate families of solutions for each element.
In this paper the application of separation of variable techniques to "convex" elements is presented.