共查询到20条相似文献,搜索用时 109 毫秒
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利用对称性约化的直接法,给出了具有非线性色散情况下的K(m,n)模型的所有对称性约化.从第一种约化方程的Painlev啨性质分析可知,K(m,n)模型仅当m=n+1和m=n+2时是可积的.特殊情况下(行波约化),这种约化的解可用一个积分表示.给出了K(m,1)和K(m,m)的一般孤波解的明显表达式.
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《物理学报》2020,(1)
本文研究了四阶色散非线性薛定谔方程的明暗孤立波和怪波的形成机制,该模型既可以模拟高速光纤传输系统中超短脉冲的非线性传输和相互作用,又可以描述具有八极与偶极相互作用的一维海森堡铁磁链的非线性自旋激发现象.本文首先通过对四阶色散非线性薛定谔方程的相平面分析,发现由其约化得到的二维平面自治系统具有同宿轨道和异宿轨道,并在相应条件下求得了方程的明孤立波解和暗孤立波解,从而揭示了同异宿轨道和孤立波解的对应关系;其次,基于非零背景平面上的精确一阶呼吸子解,给出了呼吸子的群速度和相速度的显式表达式,进而分析得出呼吸子的速度存在跳跃现象.最后,为了验证在跳跃点处呼吸子可以转化为怪波,将呼吸子解在速度跳跃条件下取极限获得了一阶怪波解,从而证实怪波的产生与呼吸子速度的不连续性有关. 相似文献
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应用经典李群理论考虑了描述非平面冲击波形成和衰减现象的(1 1)维变系数Burgers方程,得到该方程的群分类及相应的对称.对于某些具体形式的色散项系数a(t)和非线性项系数b(t),给出了对应方程的对称约化及相似解.本文在已有基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义. 相似文献
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With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS) equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations. 相似文献
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The residual symmetries of the famous modified Korteweg-de Vries (mKdV) equation are researched in this paper. The initial problem on the residual symmetry of the mKdV equation is researched. The residual symmetries for the mKdV equation are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries by means of enlarging the mKdV equations. One-parameter invariant subgroups and the invariant solutions for the extended system are listed. Eight types of similarity solutions and the reduction equations are demonstrated. It is noted that we researched the twofold residual symmetries by means of taking the mKdV equation as an example. Similarity solutions and the reduction equations are demonstrated for the extended mKdV equations related to the twofold residual symmetries. 相似文献
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The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants. 相似文献
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This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. 相似文献
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Lie Point Symmetries and Exact Solutions of Couple KdV Equations 总被引:4,自引:0,他引:4
QIAN Su-Ping TIAN Li-Xin 《理论物理通讯》2007,47(4):582-586
The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc. 相似文献
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Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption 总被引:1,自引:0,他引:1
The generalized
conditional symmetry and sign-invariant approaches are developed
to study the nonlinear diffusion equations with x-dependent
convection and source terms. We obtain conditions under which the
equations admit the second-order generalized conditional
symmetries and the first-order sign-invariants on the solutions.
Several types of different generalized conditional symmetries and
first-order sign-invariants for the equations with diffusion of
power law are obtained. Exact
solutions to the resulting equations are constructed. 相似文献
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Mustafa Inc Abdullahi Yusuf Aliyu Isa Aliyu Dumitru Baleanu 《Optical and Quantum Electronics》2018,50(4):190
This research presents soliton solutions and stability analysis to some conformable nonlinear partial differential equations (CNPDEs). The CNPDEs equations in this paper are conformable Cahn–Allen and conformable Zoomeron equations. The powerful sine-Gordon method is used to carry out the soliton solutions for these equations. The aspects of stability analysis for the considered equations is investigated using the linear stability technique. The sine-Gordon method proves to be efficient and effective for the extraction of soliton solutions for different types of CNPDEs. 相似文献
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It is shown that compatible symplectic structures lead in a natural way to hereditary symmetries. (We recall that a hereditary symmetry is an operator-valued function which immediately yields a hierarchy of evolution equations, each having infinitely many commuting symmetries all generated by this hereditary symmetry. Furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations). This result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations.In addition we show how symplectic structures transform under Bäcklund transformations. This leads to a method for generating a whole class of symplectic structures from a given one.Several examples and applications are given illustrating the above results. Also the connection of our results with those of Gelfand and Dikii, and of Magri is briefly pointed out. 相似文献
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Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. 相似文献