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利用一个独立变换和动力系统方法对Fokas方程:u_(tx)=(1+v(?)■_x~2)sin(u),x∈R,t0进行研究.在对该方程所对应的平面动力系统进行定性分析的基础上,得到了该方程所有可能的显式孤立尖波解和周期尖波解. 相似文献
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KdV方程的第二次导出 总被引:2,自引:1,他引:1
王丽霞 《数学的实践与认识》2006,36(8):345-349
考察R ay le igh1876年关于孤立波的论文及其影响.R ay le igh独立得到了与K dV方程等价的孤立波方程及其孤立波解,建立了比较合理的孤立波近似理论;他的这一工作对于人们认识孤立波的存在性产生积极影响,并对K ortew eg和de V ries1895年的论文有重要影响. 相似文献
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张平 《数学的实践与认识》2009,39(7)
应用改进的Fan's代数方法,得到了KK方程和改进的Boussinesq方程的一系列新精确解,包括孤立波解、类孤立波解、纽结波解、奇异纽结波解和三角函数周期解. 相似文献
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《数学的实践与认识》2020,(15)
主要研究了广义(2+1)维的Hirota-Satsuma-Ito(HSI)方程行波解的分岔及其动力学行为.基于行波变换,文章推导出(2+1)维广义HSI方程对应的平面动力系统.通过对平面动力系统参数不同取值的讨论,确定系统的奇点的个数和类型,得到了动力系统的轨线图.根据系统分岔情况,求解了广义的(2+1)维HSI方程相对应动力系统的不同轨线所有行波解的解析表达式,并作图展示了三类孤立波—bell型孤立波,暗孤立波和线周期波的具体性状. 相似文献
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本文研究有限水深两层流中孤立波的三阶近似理论,并考虑了自由表面对孤立波的影响,运用坐标变形方法得到了三阶内孤立波的发展方程,求得波速的解析表达式。对方程进行了数值计算,得到了几种参数下三阶解曲线,指出自由表面对波型和波速的影响是二阶的。计算表明三阶解对一阶、二阶解有明显的改进,使其更加接近试验结果。 相似文献
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线性流形上反埃尔米特广义汉密尔顿矩阵的最小二乘问题与最佳逼近问题 总被引:2,自引:1,他引:1
利用反埃尔米特广义汉密尔顿矩阵的表示定理,得到了线性流形上反埃尔米特广义汉密尔顿矩阵反问题的最小二乘解的一般表达式,建立了线性矩阵方程在线性流形上可解的充分必要条件.对于任意给定的n阶复矩阵,证明了相关最佳逼近问题解的存在性与惟一性,并推得了最佳逼近解的表达式. 相似文献
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《Chaos, solitons, and fractals》2005,23(1):159-169
We introduce a fifth-order K(m,n,1) equation with nonlinear dispersion to obtain multi-compacton solutions by Adomian decomposition method. Using the homogeneous balance (HB) method, we derive a Backlund transformation of a special equation K(2,2,1) to determine some solitary solutions of the equation. To study the stability of multi-compacton solutions in K(m,n,1) and to obtain some conservation laws, we present a similar fifth-order equation derived from Lagrangian. We finally show the linear stability of all obtained multi-compacton solutions. 相似文献
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H. A. Levine R. A. Smith L. E. Payne 《Mathematical Methods in the Applied Sciences》1987,9(1):127-136
The present paper employs potential well arguments of a previous work by the authors [6] to obtain a sharp existence-nonexistence alternative for solutions to the linear heat equation subject to a non-linear boundary condition. 相似文献
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Zuosheng Hu Angelo B. Mingarelli 《Proceedings of the American Mathematical Society》2004,132(2):417-428
We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.
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Anwar Ja’afar Mohamad-JawadMarko D. Petkovi? Anjan Biswas 《Applied mathematics and computation》2011,217(16):7039-7047
This paper applies the variational iteration method (VIM) and semi-inverse variational principle to obtain solutions of linear and nonlinear partial differential equations. The nonlinear model is considered from gas dynamics, fluid dynamics and Burgers equation. The linear model is the heat transfer (diffusion) equation. Results show that variational iteration method is a powerful mathematical tool for solving linear and nonlinear partial differential equations, and therefore, can be widely applied to engineering problems. 相似文献
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In this paper, the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion (G-BSDE for short), with the generator growing quadratically in the second unknown. The authors obtain the existence by the penalty method, and some a priori estimates which imply the uniqueness, for solutions of the G-BSDE. Moreover, focusing their discussion at the Markovian setting, the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(2):641-646
This paper considers series solutions of the Sharma–Tasso–Olver (STO) equation. By using the extended homogenous balance method, we reduce the STO equation to a linear PDE and obtain Bäcklund transformation of it. Furthermore, the self-transformation of solutions for the STO equation is obtained. By the Bäcklund transformation and various series solutions of the PDE, abundant exact solutions of the STO equation are obtained including the multi-solitary wave solution, trigonometric function series solution, rational series solution and solution consisting of the three types of solutions. 相似文献
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Karen Yagdjian 《Journal of Mathematical Analysis and Applications》2007,336(2):1259-1286
We investigate the issue of existence of the self-similar solutions of the generalized Tricomi equation in the half-space where the equation is hyperbolic. We look for the self-similar solutions via the Cauchy problem. An integral transformation suggested in [K. Yagdjian, A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain, J. Differential Equations 206 (2004) 227-252] is used to represent solutions of the Cauchy problem for the linear Tricomi-type equation in terms of fundamental solutions of the classical wave equation. This representation allows us to prove decay estimates for the linear Tricomi-type equation with a source term. Obtained in [K. Yagdjian, The self-similar solutions of the Tricomi-type equations, Z. Angew. Math. Phys., in press, doi:10.1007/s00033-006-5099-2] estimates for the self-similar solutions of the linear Tricomi-type equation are the key tools to prove existence of the self-similar solutions. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2445-2455
The Bäcklund transformations and abundant explicit exact solutions to the AKNS shallow water wave equation are obtained by combining the extended homogeneous balance method with the extended hyperbolic function method. The solutions obtained admit of multiple arbitrary parameters. These solutions include (a) a compound of the rational fractional function and a linear function, (b) a compound of solitary wave solution and a linear function, (c) a compound of the singular travelling wave solutions and a linear function, and (d) a compound of the periodic wave solutions of triangle function and a linear function. In special cases, we can obtain a series of soliton solutions, singular travelling wave solutions, periodic travelling wave solutions, and rational fractional function solution. In addition to re-deriving some known solutions in a systematic way, some brand-new exact solutions are also established. 相似文献
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Chen Lüping 《数学物理学报(B辑英文版)》2006,26(4):679-690
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C(1) smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation. 相似文献