共查询到20条相似文献,搜索用时 46 毫秒
1.
Yin Zheng 《Physics letters. A》2008,372(23):4141-4143
This Letter deals with a generalized Camassa-Holm equation and a nonlinear dispersive equation by making use of a mathematical technique based on using integral factors for solving differential equations. The peakons, solitary patterns and periodic solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are highlighted. 相似文献
2.
With the assistance of the symbolic
computation system Maple, rich higher order polynomial-type
conservation laws and a sixth order t/x-dependent conservation
law are constructed for a generalized seventh order nonlinear
evolution equation by using a direct algebraic method. From the
compatibility conditions that guaranteeing the existence of
conserved densities, an integrable unnamed seventh order KdV-type
equation is found. By introducing some nonlinear transformations,
the one-, two-, and three-solition solutions as well as the
solitary wave solutions are obtained. 相似文献
3.
Haci Mehmet Baskonus Tukur Abdulkadir Sulaiman Hasan Bulut 《Optical and Quantum Electronics》2018,50(6):253
In this paper, we study the generalized higher-order nonlinear Schrödinger equation analytically. We use two integral schemes for conducting this study. Dark, bright, combined dark–bright optical, singular soliton, soliton-like and trigonometric function solutions are successfully constructed. We give the constraint conditions for the existence of valid solutions. The 2D, 3D and the contour graphs for the dark and bright solitons are plotted. 相似文献
4.
5.
Herein, an efficient numerical method is presented to describe the flow of a liquid in an open channel with various types of bottom configurations. The method is developed for steady two-dimensional potential free surface flows. The resulting nonlinear problem is solved numerically by boundary integral equation methods. In addition weakly nonlinear solutions are derived. New solutions which complement those of Dias and Vanden-Broeck [J. Fluid Mech. 59, 93-102 (2004)] are presented. Furthermore some solutions for channel flows past dips in the bottom are discussed. 相似文献
6.
A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods 下载免费PDF全文
Hongqiang Zhu Yue Cheng & Jianxian Qiu 《advances in applied mathematics and mechanics.》2013,5(3):365-390
Discontinuities usually appear in
solutions of nonlinear conservation laws even though the initial
condition is smooth, which leads to great difficulty in computing
these solutions numerically. The Runge-Kutta discontinuous Galerkin
(RKDG) methods are efficient methods for solving nonlinear
conservation laws, which are high-order accurate and highly
parallelizable, and can be easily used to handle complicated
geometries and boundary conditions. An important component of RKDG
methods for solving nonlinear conservation laws with strong
discontinuities in the solution is a nonlinear limiter, which is
applied to detect discontinuities and control spurious oscillations
near such discontinuities. Many such limiters have been used in the
literature on RKDG methods. A limiter contains two parts, first to
identify the "troubled cells", namely, those cells which might
need the limiting procedure, then to replace the solution
polynomials in those troubled cells by reconstructed polynomials
which maintain the original cell averages (conservation). [SIAM
J. Sci. Comput., 26 (2005), pp. 995-1013] focused on discussing the
first part of limiters. In this paper, focused on the second part,
we will systematically investigate and compare a few different
reconstruction strategies with an objective of obtaining the most
efficient and reliable reconstruction strategy. This work can help
with the choosing of right limiters so one can resolve sharper
discontinuities, get better numerical solutions and save the
computational cost. 相似文献
7.
利用拉格朗日方程建立了单质点弹簧振子非线性振动方程,作出了回复力、势能随坐标的变化曲线以及相图.应用第一类完全椭圆积分求出了非线性振动周期的精确解.应用线化和校正法对单质点弹簧振子的周期和近似解进行了求解.利用Maple计算机绘图,分别作出了它们的周期近似解与周期精确解随振幅的变化曲线以及近似解与数值解的变化曲线.利用线化和校正法所求得的近似解与数值解比较,具有简单实用、精度高、相对误差低等优点,在求解非线性振动中具有一定的实用价值. 相似文献
8.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential 下载免费PDF全文
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation. 相似文献
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10.
Unified treatment of the bound states of the Schioberg and the Eckart potentials using Feynman path integral approach 下载免费PDF全文
We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term.In order to determine the e-states solutions,we use the Feynman path integral approach to quantum mechanics.We show that by performing nonlinear space-time transformations in the radial path integral,we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system.The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions.We show that the Eckart potential can be derived from the Schioberg potential.The obtained results are compared to those produced by other methods and are found to be consistent. 相似文献
11.
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211–228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss–Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature. 相似文献
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13.
Bashir Ahmad Ahmed Alsaedi Hana Al-Hutami 《Central European Journal of Physics》2013,11(10):1487-1493
This paper investigates the existence of solutions for a nonlinear boundary value problem of sequential fractional differential equations with four-point nonlocal Riemann-Liouville type fractional integral boundary conditions. We apply Banach’s contraction principle and Krasnoselskii’s fixed point theorem to establish the existence of results. Some illustrative examples are also presented. 相似文献
14.
While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones. 相似文献
15.
In this paper, conservation laws and exact solution are found for nonlinear Schrödinger–Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger–Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering. 相似文献
16.
Some new exact solutions to the Burgers--Fisher equation and generalized Burgers--Fisher equation 下载免费PDF全文
Some new exact solutions of the Burgers--Fisher equation and
generalized Burgers--Fisher equation have been obtained by using the
first integral method. These solutions include exponential function
solutions, singular solitary wave solutions and some more complex
solutions whose figures are given in the article. The result shows
that the first integral method is one of the most effective
approaches to obtain the solutions of the nonlinear partial
differential equations. 相似文献
17.
In this paper, the modulation instability(MI), rogue waves(RWs) and conservation laws of the coupled higher-order nonlinear Schr?dinger equation are investigated. According to MI and the2?×?2 Lax pair, Darboux-dressing transformation with an asymptotic expansion method, the existence and properties of the one-, second-, and third-order RWs for the higher-order nonlinear Schr?dinger equation are constructed. In addition, the main characteristics of these solutions are discussed through some graphics, which are draw widespread attention in a variety of complex systems such as optics, Bose–Einstein condensates, capillary flow, superfluidity, fluid dynamics,and finance. In addition, infinitely-many conservation laws are established. 相似文献
18.
R. O. Barrachina 《Journal of statistical physics》1988,52(1-2):357-368
The relaxation to equilibrium of a spatially uniform pseudo-Maxwellian gas is considered. A modified Wild expansion is defined for solving the nonlinear Boltzmann equation. The positivity and asymptotic conditions, as well as the conservation rules, are maintained at each truncation order. Some particular examples are evaluated. The comparison with exact solutions illustrates the very fast convergence of this method. 相似文献
19.
《中国物理快报》2016,(7)
This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation.Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays,a more general model equation and integral forms of quasilinear solutions are introduced.Some features of steered and focused beam Gelds radiated from a linear phased array of the second harmonic Rayleigh wave are presented. 相似文献
20.
U. Weiss 《Zeitschrift für Physik B Condensed Matter》1978,30(4):429-436
A method is given for the derivation of covariant path integral solutions of quantum and stochastic processes in curved space.The correspondence between operator ordering schemes and ordinary functions in phase space is studied and applied to the explicit construction of a class of equivalent lattice representations of path integrals. It is shown that this class is uniquely related to a covariant functional integral. Some arguments forR/12 as the quantum mechanical curvature potential are given. Simple rules for nonlinear point transformations are stated. The connection with previous works is discussed. 相似文献