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In this paper, the resonant nonlinear Schrödinger's equation is studied with three forms of nonlinearity. This equation is also considered with time-dependent coefficients. The first integral method is used to carry out the integration. Exact soliton solutions of this equation are found. These solutions are constructed through the established first integrals. The power of this manageable method is confirmed. 相似文献
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Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order 下载免费PDF全文
In this paper, the travelling wave solutions for the generalized
Burgers--Huxley equation with nonlinear terms of any order are
studied. By using the first integral method, which is based on the
divisor theorem, some exact explicit travelling solitary wave
solutions for the above equation are obtained. As a result, some
minor errors and some known results in the previousl literature
are clarified and improved. 相似文献
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This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained. 相似文献
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In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method. 相似文献
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Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order 下载免费PDF全文
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. 相似文献
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Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order 下载免费PDF全文
In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. 相似文献
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V. I. Zhdanov 《Russian Physics Journal》1981,24(7):619-623
A method is proposed for studying the low-frequency solutions of Teukolsky's equation, describing the behavior of massless fields in the vicinity of a Kerr black hole. Approximate basis solutions and an integral equation for exact solutions are constructed. The analytic properties of the exact solutions and the asymptotic behavior of the leading nonanalytic parts are investigated and the approximate solutions are estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 47–51, July, 1981.The author is grateful to Professor K. A. Piragas and the participants of the seminar directed by him for their attention to the present work and for useful discussions. 相似文献
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A. Kim 《Waves in Random and Complex Media》2005,15(1):17-42
The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law. 相似文献
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《Waves in Random and Complex Media》2013,23(4):536-548
Given the application of inhomogeneous and anisotropic structures in different application areas, it is of critical importance to develop accurate and efficient modeling methods. Among various methods, volume integral equations (VIEs) using moment method are efficient solutions for electromagnetic modeling of inhomogeneous and anisotropic structures. In this paper, we investigate the solutions of the VIE method and augmented volume integral equation (A-VIE) method for solving inhomogeneous and anisotropic structures with arbitrary shapes. The moment method solutions are presented and curl-conforming bases are used to discretize the electric and magnetic field distributions inside the structures. When the structures contain inhomogeneous magnetic materials, A-VIE method is applied. Various numerical examples are shown to demonstrate the accuracy and efficiency of the algorithms. 相似文献
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Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied. 相似文献
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The 1-dimensional non-homogeneous material balance equation has been examined in the rectangular, spherical and cylindrical
coordinate system. The solutions to this equation in the respective coordinate system has been determined analytically using
the method of integral transform, together with the norms and eigen values suitable for galvanostatic discharge boundary conditions. 相似文献
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J. Honerkamp 《Communications in Mathematical Physics》1968,7(3):234-260
The Bethe-Salpeter equation describing the interaction of two scalar particles via the exchange of a third scalar particle with mass 0 is in configuration space a hyperbolic partial differential equation of fourth order which will be studied with the help of the Riemann method. This method yields two Volterra equations the solutions of which are special solutions of the Bethe-Salpeter equation. The wave function is a superposition of the special solutions. For the coefficients one gets a system of two integral equations. The Fredholm determinant of the system is the generalization of the nonrelativistic Jost function. 相似文献
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《Waves in Random and Complex Media》2013,23(1):17-42
The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law. 相似文献