共查询到20条相似文献,搜索用时 31 毫秒
1.
The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献
2.
Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split
system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex
heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie
symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the
complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute
a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed
by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial
differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential
equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition
that gives the criteria when the Lie-like operators are symmetries of the split system. 相似文献
3.
Emmanuel Yomba 《Physics letters. A》2009,373(44):4001-4011
An algorithm is devised for deriving exact traveling wave solutions of a three-component system of nonlinear Schrödinger (NLS) equations by means of Exp-function method. This method was previously applied to nonlinear partial differential equations (NLPDEs) or two coupled NLPDEs, here it is applied to three coupled NLPDES. This work continues to reinforce the idea that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear partial differential equations. 相似文献
4.
5.
《Physics letters. A》2020,384(2):126064
The hodograph transformation is generally used in order to associate a system of linear partial differential equations to a system of nonlinear (quasilinear) differential equations by interchanging dependent and independent variables. Here we consider the case when the nonlinear differential system can be derived from a Lagrangian density and revisit the hodograph transformation within the formalism of the Lagrangian-Hamiltonian continuous dynamical systems.Restricting to the case of nondissipative, nondispersive one-dimensional waves, we show that the hodograph transformation leads to a linear partial differential equation for an unknown function that plays the role of the Lagrangian in the hodograph variables. We then define the corresponding hodograph Hamiltonian and show that it turns out to coincide with the wave amplitude. i.e., with the unknown function of the independent variables to be solved for in the initial nonlinear wave equation. 相似文献
6.
Hiroshi Shibata 《Physica A》1998,260(3-4)
Disorderness of spatiotemporal patterns which are obtained by nonlinear partial differential equations is characterized quantitatively. The mean Lyapunov exponent for a nonlinear partial differential equation is given. The local Lyapunov exponent which is a finite time average of the mean Lyapunov exponent is shown to have close relation to the spatiotemporal patterns. It is suggested that the systems which are described by nonlinear partial differential equations are characterized statistically through the probability distribution function of the local Lyapunov exponent. 相似文献
7.
The application of transformation group methods to a system of nonlinear partial differential equations, representing an incompressible M H D plasma, is shown. The structure of the symmetry group is investigated and a theorem of existence of the solutions of the system of equations is given. Some illustrative analytical invariant solutions and their differential invariants will be presented. 相似文献
8.
S. I. Pokhozhaev 《Russian Journal of Mathematical Physics》2013,20(4):476-491
The paper is devoted to the role of critical nonlinearities in the framework of the theory of global solvability of nonlinear partial differential equations. In particular, a new approach to blow-up problems for solutions of nonlinear partial differential equations is suggested. 相似文献
9.
Motivated by the widely used ansätz method and starting from the modified Riemann-Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. 相似文献
10.
The homogeneous balance principle has been widely applied to the exploration of nonlinear transformation, exact solutions (especially solitary wave solution), dromion and similarity reduction to the nonlinear partial differential equations in mathematical physics. In this paper, we use the homogeneous balance principle to derive B?cklund transformations for nonlinear partial differential equations that have more nonlinear terms and more highest-order partial derivative terms. With the aid of the B?cklund transformations derived here, we could obtain exact solutions to the nonlinear partial differential equations. The Davey-Stewartson equation and the Nizhnik-Novikov-Veselov equation are considered as the examples. 相似文献
11.
The subject of this paper is the development of a general solution procedure for the vibrations (primary resonance and nonlinear natural frequency) of systems with cubic nonlinearities, subjected to nonlinear and time-dependent internal boundary conditions—this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements. The equations of motion form a set of nonlinear partial differential equations with nonlinear, time-dependent, and coupled internal boundary conditions. The method of multiple timescales, an approximate analytical method, is applied directly to each partial differential equation of motion as well as coupled boundary conditions (i.e. on each sub-domain and the corresponding internal boundary conditions for a continuous system with intermediate elements) which ultimately leads to approximate analytical expressions for the frequency-response relation and nonlinear natural frequencies of the system. These closed-form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system. Moreover, the suggested solution procedure is applied to a sample problem which is discussed in detail. 相似文献
12.
In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp (?φ(η))-expansion method is implemented to find exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effective and can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method provides additional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order and could be protracted to other physical phenomena. 相似文献
13.
Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential
evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution
equations were lifted to the corresponding functional partial differential equations in functional space by introducing the
time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The
algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact
analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution
equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer
numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic
dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution
equations both analytically and numerically.
Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program
Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China 相似文献
14.
The Exp-function method with the aid of symbolic computational system is used to obtain the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, nonlinear partial differential (BBMB) equation, generalized RLW equation and generalized shallow water wave equation. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics. 相似文献
15.
By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated. 相似文献
16.
DAI Chao-Qing ZHANG Jie-Fang 《理论物理通讯》2006,46(7)
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach. 相似文献
17.
DAI Chao-Qing ZHANG Jie-Fang 《理论物理通讯》2006,46(1):23-27
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach. 相似文献
18.
Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations 总被引:2,自引:2,他引:0
The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms
of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary
differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,
and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential
equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is
described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like
solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and
its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm
and Symplectic Geometric Algorithm. 相似文献
19.
A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given. 相似文献
20.
Mergen H. Ghayesh 《Journal of sound and vibration》2012,331(23):5107-5124
The coupled longitudinal–transverse nonlinear dynamics of an axially accelerating beam is numerically investigated; this problem is classified as a parametrically excited gyroscopic system. The axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations. Hamilton’s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations. The equations are discretized using the Galerkin method, which yields a set of coupled second-order nonlinear ordinary differential equations with time-dependent coefficients. The sub-critical dynamics of the system is examined via the pseudo-arclength continuation technique, while the global dynamics is investigated using direct time integration. The mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of Poincaré maps. The vibration specifications of the system are investigated more detailed via plotting time histories, phase-plane portraits, and fast Fourier transforms (FFTs). 相似文献