共查询到20条相似文献,搜索用时 15 毫秒
1.
A. Bekir 《Physics of Wave Phenomena》2012,20(2):118-121
It is established abundant one- and two-soliton solutions to nonlinear Cahn-Allen equation. It is shown that the double exp-function method, with the help of symbolic computation, provides a very effective and powerful new tool for solving nonlinear evolution equations in mathematical physics. 相似文献
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In this paper, the exp-function method is generalized to sine-Gordon (sG) equation and single-, double- and three-wave solutions are obtained. It is shown that the generalized exp-function method combined with appropriate anstaz may provide a straightforward, effective and alternative method for constructing multiwave solutions of some nonlinear partial differential equations. 相似文献
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This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics. 相似文献
5.
Jun-ting Pan 《Physics letters. A》2009,373(35):3118-3121
A new auxiliary equation method, constructed by a first order nonlinear ordinary differential equation with at most an eighth-degree nonlinear term, is first proposed for exploring more exact solutions to nonlinear evolution equations. Being concise and straightforward, the method, with the aid of symbolic computation, is applied to the Sharma-Tasso-Olver model, and some new exact solitary wave solutions are obtained. The approach is also applicable to searches for exact solutions of other nonlinear evolution equations. 相似文献
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We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model. 相似文献
8.
Ranjit Kumar 《Pramana》2012,79(3):393-402
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences. 相似文献
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Emmanuel Yomba 《Physics letters. A》2008,372(7):1048-1060
With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions. 相似文献
12.
Some new solitary and travelling wave solutions of certain nonlinear diffusion-reaction equations using auxiliary equation method 总被引:1,自引:0,他引:1
Attempts are made to look for the soliton content in the exact solutions of certain types of nonlinear diffusion-reaction (DR) equations with the quadratic and cubic nonlinearities. Such equations may arise in a variety of contexts in physical problems. In this Letter using the auxiliary equation method, some new solitary and travelling wave solutions of such nonlinear DR equations are obtained in a very general form. Several interesting special cases of these general solutions are also discussed. 相似文献
13.
Yang SA 《The Journal of the Acoustical Society of America》2002,112(4):1307-1317
This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method. 相似文献
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《Physics letters. A》2006,356(2):124-130
A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein–Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham–Broer–Kaup equations. 相似文献
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S.A. Elwakil 《Journal of Quantitative Spectroscopy & Radiative Transfer》2003,77(3):317-327
The operator method has been used to solve the fractional Fokker-Planck equation (FPE) which recently formulated as a model for the anomalous transport process. Two classes of special interest of fractional F-P equations coming from plasma physics and charged particle transport problem has been considered. It is shown that the mean square-displacement 〈x2(t)〉 satisfy the universal power law characterized the anomalous time evolution i.e. . 相似文献
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Van Hove's partial density matrix,
E
(t), in his generalized master equation is interpreted as a Wigner representation of two-time dyad for energy E and time t. This interpretation enables us to integrate the energyE in Van Hove's master equation. The resultant equation is of non-Markov type on two time parameters. Starting with this master equation, the derivation of quantum kinetic equations, including the second-order approximation in the density expansion, is discussed. The scaling of the quantum kinetic equation is examined in detail for a system in which particles interact through the delta shell potential. It is shown that the quantum kinetic equation, including three-particle scattering, may exist for the physical situations of low-energy scattering,high-energy scattering, and for resonance scattering for time scales of the system sufficiently separated. In deriving the quantum kinetic equation, a factorization theorem form-particle distribution functions is proved to arbitrary order in perturbation expansion. 相似文献
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Radiophysics and Quantum Electronics - 相似文献
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A steady-state model has been considered to explain the observed properties of the LSSS RXJ0925.7-4748 / MR Vel. The steady-state models consist of a C–O core surrounded by a hydrogen-rich envelope of the solar abundances. At the bottom of the envelope, hydrogen is burned at the same rate as the star accreted it. Using the most recent proton capturing reaction rates and \(\beta \)-decay rates, the cyclic reactions have been studied. In the present work, effort has been made to explain the observed characteristics of the source RXJ0925.7-4758 / MR Vel considering the above mentioned model. The calculated values of luminosity (\(8.56 \times 10^{37} \, \hbox {erg}\,\hbox {s}^{-1}\)) and effective temperature (94.19 eV) tally well with the observed one. Photoionisation code CLOUDY has been used to explain the observed absorption edges in the spectrum of RXJ0925.7-4758 / MR Vel. 相似文献
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We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization. 相似文献
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V. V. Rubish V. Yu. Lazur O. K. Reity S. Chalupka M. Salak 《Czechoslovak Journal of Physics》2004,54(9):897-919
The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The
relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For
spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated.
Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done. 相似文献