共查询到19条相似文献,搜索用时 78 毫秒
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利用扰动法由准地转涡度方程导出了强迫mKdV方程,讨论了强迫mKdV孤波的质量和能量的时间演变,并通过拟谱法求得了强迫mKdV方程的数值解。计算结果显示,局地外源强迫激发的mKdV孤波与失谐参数α和外源强度有密切关系。与强迫KdV方程相比,在强迫mKdV方程中,外源强迫可以激发出振幅更大的更不稳定的孤波。 相似文献
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利用数值方法研究了双温离子、磁场、非均匀性和波的斜向传播对三维非线性尘埃声孤波振幅和宽度的影响。运用约化摄动法得到描述三维非线性尘埃声孤波的非标准变系数Korteweg-de Vries(KdV)方程。然后把非标准变系数KdV方程变为标准变系数KdV方程,并且得到了此标准变系数KdV方程的近似解析解。研究结果表明,此系统中存在着两种形式的孤波,即压缩型孤波和稀疏型孤波,外部磁场对三维非线性尘埃声孤波的宽度有影响,而对其振幅没有影响。此外,波的相速度与波的斜向传播和非均匀性有着非常紧密的联系。 相似文献
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Higher-Dimensional KdV Equations and Their Soliton Solutions 总被引:2,自引:0,他引:2
A (2+1)-dimensional KdV equation is obtained by use of Hirota
method, which possesses N-soliton solution, specially its exact
two-soliton solution is presented. By employing a proper algebraic
transformation and the Riccati equation, a type of bell-shape
soliton solutions are produced via regarding the variable in the
Riccati equation as the independent variable. Finally, we extend
the above (2+1)-dimensional KdV equation into (3+1)-dimensional
equation, the two-soliton solutions are given. 相似文献
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New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 总被引:1,自引:0,他引:1
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(11)
In this paper, the generalized tanh function method is extended to (2 1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2 1)-dimensional CGKP equation with variable coefficients. 相似文献
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This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed. 相似文献
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ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(5):793-798
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 相似文献
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The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics
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Using the projective Riccati equation expansion (PREE) method, new
families of variable separation solutions (including solitary wave
solutions, periodic wave solutions and rational function solutions)
with arbitrary functions for two nonlinear physical models are
obtained. Based on one of the variable separation solutions and by
choosing appropriate functions, new types of interactions between
the multi-valued and single-valued solitons, such as a peakon-like
semi-foldon and a peakon, a compacton-like semi-foldon and a
compacton, are investigated. 相似文献
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Emad A-B. ABDEL-SALAM 《理论物理通讯》2009,52(6):1004-1012
By introducing the Lucas--Riccati method and a linear variable separationmethod, new variable separation solutions with arbitrary functions arederived for a (2+1)-dimensional modified dispersive water-wave system. Themain idea of this method is to express the solutions of this system aspolynomials in the solution of the Riccati equation that the symmetricalLucas functions satisfy. From the variable separation solution and byselecting appropriate functions, some novel Jacobian elliptic wave structurewith variable modulus and their interactions with dromions and peakons are investigated. 相似文献
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New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients 总被引:1,自引:0,他引:1
CHENHuai-Tang ZHANGHong-Qing 《理论物理通讯》2004,42(4):497-500
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1)-dimensional Burgers equation with variable coefficients. 相似文献
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New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients
CHEN Huai-Tang ZHANG Hong-Qing 《理论物理通讯》2004,42(10)
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1 )-dimensional Burgers equation with variable coefficients. 相似文献