共查询到20条相似文献,搜索用时 156 毫秒
1.
Elham Lashkarian S. Reza Hejazi Elham Dastranj 《Computers & Mathematics with Applications》2018,75(3):740-754
The concept of Lie–Backlund symmetry plays a fundamental role in applied mathematics. It is clear that in order to find conservation laws for a given partial differential equations (PDEs) or fractional differential equations (FDEs) by using Lagrangian function, firstly, we need to obtain the symmetries of the considered equation.Fractional derivation is an efficient tool for interpretation of mathematical methods. Many applications of fractional calculus can be found in various fields of sciences as physics (classic, quantum mechanics and thermodynamics), biology, economics, engineering and etc. So in this paper, we present some effective application of fractional derivatives such as fractional symmetries and fractional conservation laws by fractional calculations. In the sequel, we obtain our results in order to find conservation laws of the time-fractional equation in some special cases. 相似文献
2.
Jiangen Liu Yufeng Zhang Iqbal Muhammad 《Computers & Mathematics with Applications》2018,75(11):3939-3945
In this letter, the linear superposition principle is used to discuss the -dimensional Boiti–Leon–Manna–Pempinelli equation with bilinear derivatives. As a result, we obtain new resonant soliton and complexiton solutions by discussing two different cases involved the parameters. These solutions are a class of -wave solutions of linear combinations of exponential traveling waves. 相似文献
3.
Xiaojun Yin Liangui Yang Quansheng Liu Guorong Wu 《Computers & Mathematics with Applications》2019,77(1):302-310
The (1 +1)-dimensional mathematical model had been extensively derived to describe Rossby solitary waves in a line in the past few decades. But as is well known, the (1 +1)-dimensional model cannot reflect the generation and evolution of Rossby solitary waves in a plane. In this paper, a (2 +1)-dimensional nonlinear Zakharov–Kuznetsov–Burgers equation is derived to describe the evolution of Rossby wave amplitude by using methods of multiple scales and perturbation expansions from the quasi-geostrophic potential vorticity equations with the generalized beta effect. The effects of the generalized beta and dissipation are presented by the Zakharov–Kuznetsov–Burgers equation. We also obtain the new solitary solution of the Zakharov–Kuznetsov equation when the dissipation is absent with the help of the Bernoulli equation, which is different from the common classical solitary solution. Based on the solution, the features of the variable coefficient are discussed by geometric figures Meanwhile, the approximate solitary solution of Zakharov–Kuznetsov–Burgers equation is given by using the homotopy perturbation method. And the amplitude of solitary waves changing with time is depicted by figures. Undoubtedly, these solitary solutions will extend previous results and better help to explain the feature of Rossby solitary waves. 相似文献
4.
Wenqiang Zhao 《Computers & Mathematics with Applications》2018,75(10):3801-3824
In this article, we use the so-called difference estimate method to investigate the continuity and random dynamics of the non-autonomous stochastic FitzHugh–Nagumo system with a general nonlinearity. Firstly, under weak assumptions on the noise coefficient, we prove the existence of a pullback attractor in by using the tail estimate method and a certain compact embedding on bounded domains. Secondly, although the difference of the first component of solutions possesses at most -times integrability where is the growth exponent of the nonlinearity, we overcome the absence of higher-order integrability and establish the continuity of solutions in with respect to the initial values belonging to . As an application of the result on the continuity, the existence of a pullback attractor in is proved for arbitrary and . 相似文献
5.
Sean Breckling Monika Neda Fran Pahlevani 《Computers & Mathematics with Applications》2018,75(2):666-689
We present a sensitivity study of the Navier Stokes- model with respect to perturbations of the differential filter length . The parameter-sensitivity is evaluated using the sensitivity equations method. Once formulated, the sensitivity equations are discretized and computed alongside the NS model using the same finite elements in space, and Crank–Nicolson in time. We provide a complete stability analysis of the scheme, along with the results of several benchmark problems in both 2D and 3D. We further demonstrate a practical technique to utilize sensitivity calculations to determine the reliability of the NS model in problem-specific settings. Lastly, we investigate the sensitivity and reliability of important functionals of the velocity and pressure solutions. 相似文献
6.
Chun-Ku Kuo 《Computers & Mathematics with Applications》2018,75(8):2851-2857
In this paper, by employing two different simplest equation methods, the (21)-dimensional Zakharov–Kuznetsov (ZK) equation derived for describing weakly nonlinear ion-acoustic waves in the plasma is investigated. With the aid of the Bernoulli equation and the coupled Burgers’ equations, the electric field potential of ZK equation are formally obtained, which are presented as the new solitary and multi-soliton solutions. Meanwhile, the electric field and magnetic field can be accordingly obtained. In addition, the significant features of the variable coefficient and parameter are discovered. The results show that the solitary and multi-soliton solutions are precisely obtained and the efficiency of the methods is demonstrated. These new exact solutions will extend previous results and help to explain the features of nonlinear ion-acoustic waves in the plasma. 相似文献
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