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1.
After a quick review of the Lane-Emden equation and its properties, a composite of two different polytropes is introduced
and some of the consequences are explored. The results are used to build a nonlinear electromagnetism with non-singular, solitonic
solutions as charged particles. 相似文献
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This article puts forward a new way to find solutions of CDG equation. The main results are:(i) According to the Lax pair of CDG equation, we introduce the modified CDG equation. (ii) An invariance depending on two parameters of M-CDG equation is found. (iii) Some solutions for CDG equation are obtained by using the invariance. 相似文献
3.
A simple derivation of the Marchenko equation is given for the derivative nonlinear Schrodinger equation. The kernel of the Marchenko equation is demanded to satisfy the conditions given by the compatibility equations. The soliton solutions to the Marchenko equation are verified. The derivation is not concerned with the revisions of Kaup and Newell. 相似文献
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Jean Pierre Boon Patrick Grosfils James F. Lutsko 《Journal of statistical physics》2003,113(3-4):527-548
A propagation-dispersion equation is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the hydrodynamic limit of the first visit equation, an exact microscopic finite difference equation describing the motion of a particle on a lattice whose sites operate as time-delayers. The propagation-dispersion equation should be contrasted with the advection-diffusion equation (or the classical Fokker–Planck equation) as it describes a dispersion process in time (instead of diffusion in space) with a drift expressed by a propagation speed with non-zero bounded values. The temporal dispersion coefficient is shown to exhibit a form analogous to Taylor's dispersivity. Physical systems where the propagation-dispersion equation applies are discussed. 相似文献
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In this paper,the supersymmetric Camassa-Holm equation and Degasperis-Procesi equation are derived from a general superfield equations by choosing different parameters.Their peakon-type solutions are shown in weak sense.At the same time,the dynamic behaviors are analyzed particularly when the two peakons collide elastically,and some results are compared with each other between the two equations. 相似文献
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Derivation of Dirac's Equation from the Evans Wave Equation 总被引:1,自引:0,他引:1
M. W. Evans 《Foundations of Physics Letters》2004,17(2):149-166
The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector qused to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result. 相似文献
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Contrary to the conventional view, the Breit equation can be solved.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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Slobodan Prvanovi? 《International Journal of Theoretical Physics》2012,51(9):2743-2753
The symmetrized product of quantum observables is defined. It is seen as consisting of ordinary multiplication followed by application of the superoperator that orders the operators of coordinate and momentum. This superoperator is defined in the way that allows obstruction free quantization of algebra of observables as well as introduction of operator version of the Poisson bracket. It is shown that this bracket has all properties of the Lie bracket and that it can substitute the commutator in the von Neumann equation leading to quantum Liouville equation. 相似文献
14.
Based on the Waleck's models QHD-Ⅰ and QHD-Ⅱ describing the nucleon-nucleon interaction,the Boltzmann-Uehling-Uhlenbeck (BUU) equation,which is the time evolution of the nucleon distribution function including the Hartree and Fock self-energy terms as well as the Born collision term and its exchange term,has been derived by using the closed-time path Green's function technique and assuming that the Green's functions and the self-energy terms are slowly varying functions of the centre-of-mass coordinates.Our result shows that the BUU equation for proton and that for neutron are simultaneous each other. 相似文献
15.
In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained. 相似文献
16.
REN Ji RUAN Hang-Yu 《理论物理通讯》2008,50(9):575-578
We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Sehroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (CLGRM), the abundant solutions of NLSE and HONLSE are obtained. 相似文献
17.
In this paper, to construct exact solution of nonlinear partial
differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By
the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived.
We investigate the short wave model for the Camassa-Holm equation
and the Degasperis-Procesi equation respectively. One-cusp soliton
solution of the Camassa-Holm equation is obtained. One-loop soliton solution of the Degasperis-Procesi equation is also obtained, the approximation of which in a closed form can be
obtained firstly by the Adomian decomposition method. The obtained
results in a parametric form coincide perfectly with those given
in the present reference. This illustrates the efficiency and
reliability of our approach. 相似文献
18.
YANG Pei CHEN Yong LI Zhi-Bin 《理论物理通讯》2008,50(9):583-586
In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach. 相似文献
19.
The general solution to the complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special case. 相似文献
20.
The variable-coefficient generalizations of thecelebrated KP equation (GvcKPs) are realistic models forvarious physical and engineering situations. In thisnote, the application of symbolic computation and the truncated Painleve expansion leads toan auto-Backlund transformation and soliton-typedsolutions to a type of the GvcKPs. 相似文献