共查询到20条相似文献,搜索用时 328 毫秒
1.
赵露 《纯粹数学与应用数学》2018,(2):118-127
根据简化的Hirota双线性方法和cole-hopf变换,当双模Jordan KdV方程中的非线性参数与线性参数取特殊值时,得到了双模Jordan KdV方程的多孤子解.同时,当方程中非线性参数与线性参数取一般值,也得到了这个方程的其它的精确解. 相似文献
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本文建立了非线性Boltzmann输运方程与线性AKNS方程之间的直接联系,从而以不同于Chapman,Enskog和Grad的方式,使Boltzmann方程化归为Dirac方程的求解。在没有其他外场作用的情形中,Boltzmann方程的精确解可以用逆散射方法来求得。 相似文献
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Zhiber-Shabat方程的孤立波解与周期波解 总被引:1,自引:1,他引:0
结合齐次平衡法原理并利用F展开法,再次研究了Zhiber-Shabat方程的各种椭圆函数周期解.当椭圆函数的模m分别趋于1或0时,利用这些椭圆函数周期解,得到了Zhiber-Shabat方程的各种孤子解和三角函数周期解,从而丰富了相关文献中关于Zhiber-Shabat波方程的解的类型. 相似文献
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共振条件下一类方程无界解和周期解的共存性 总被引:1,自引:1,他引:0
讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性.利用Poincare映射轨道的性质,给出了无界解的存在性条件.在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的.最后,给出了一个无界解和周期解共存的具有等时位势的方程实例. 相似文献
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RLW-Burgers方程的一类解析解 总被引:1,自引:0,他引:1
谈骏渝 《数学的实践与认识》2001,31(5):545-549
本文给出了 RLW-Burgers方程及 Kd V-Burgers方程的一类解析解 ,且可得到 RLW-Burgers方程的振荡激波解 .这些解可以表示为 Burgers方程和 Kd V方程解的线性组合 ,文末还对文 [8]作了讨论 . 相似文献
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沈惠川 《数学物理学报(A辑)》1996,16(1):40-47
该文将等熵磁流体力学(MHD)或等熵电磁流体力学(EMHD)的基本方程组以及(非相对论的或相对论的)Vlasov方程,分别化为等熵流体力学(HD)表象,建立了上述三类等熵方程之间的对应关系.从而使非相对论Vlasov方程的精确解(它与等熵MHD方程的精确解相对应)和相对论Vlasov方程的精确解(它与等熵EMHD方程的精确解相对应)都可以用(非相对论的和相对论的)等熵HD方程的精确解来表示. 相似文献
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In this paper, we demonstrate that 14 solutions from 34 of the combined KdV and Schwarzian KdV equation obtained by Li [Z.T. Li, Appl. Math. Comput. 215 (2009) 2886-2890] are wrong and do not satisfy the equation. The other a number of exact solutions are equivalent each other. 相似文献
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M. N. B. Mohamad 《Mathematical Methods in the Applied Sciences》1992,15(2):73-78
This paper presents two different methods for the construction of exact solutions to the combined KdV and mKdV equation. The first method is a direct one based on a general form of solution to both the KdV and the modified KdV (mKdV) equations. The second method is a leading order analysis method. The method was devised by Jeffrey and Xu. Each of these methods is capable of solving the combined KdV and mKdV equation exactly. 相似文献
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We show that the Benjamin–Bona–Mahoney (BBM) equation with power law nonlinearity can be transformed by a point transformation to the combined KdV–mKdV equation, that is also known as the Gardner equation. We then study the combined KdV–mKdV equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the combined KdV–mKdV equation are derived. We obtain symmetry reduction and a number of exact group-invariant solutions for the underlying equation using the Lie point symmetries of the equation. The conserved densities are also calculated for the BBM equation with dual nonlinearity by using the multiplier approach. Finally, the conserved quantities are computed using the one-soliton solution. 相似文献
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Zitian Li 《Applied mathematics and computation》2009,215(8):2886-2890
In this short letter, new exact solutions including kink solutions, soliton-like solutions and periodic form solutions for a combined version of the potential KdV equation and the Schwarzian KdV equation are obtained using the generalized Riccati equation mapping method. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(1):80-87
In this work, we develop a new integrable equation by combining the KdV equation and the negative‐order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painlevé test. As a result, multiple soliton solutions and other soliton and periodic solutions are guaranteed and formally derived. 相似文献
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周汝光 《数学物理学报(A辑)》1998,18(2):228-234
基于Lax对非线性化方法,我们以KdV方程为例给出了一个构造孤子方程的有限带势解的方法.通过Lax对非线性化KdV方程被分解成两个有限维可积系统,进而找到这些有限维可积系统公共的角-作用坐标,最终我们获得了KdV方程的有限带势解. 相似文献
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In this paper, we apply the method of iterative operator splitting on the Korteweg-de Vries (KdV) equation. The method is based on first, splitting the complex problem into simpler sub-problems. Then each sub-equation is combined with iterative schemes and solved with suitable integrators. Von Neumann analysis is performed to achieve stability criteria for the proposed method applied to the KdV equation. The numerical results obtained by iterative splitting method for various initial conditions are compared with the exact solutions. It is seen that they are in a good agreement with each other. 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(3):912-919
This paper aims at presenting a proof of the existence of the attractor for the two-dimensional weakly damped KdV equations in belt field. By using the Bourgain spaces and the orthogonal projection, we prove the existence of the attractor for the reduced equation which is obtained from the two-dimensional weakly damped KdV equation in belt field. By using the time estimate of the blow-up of the KdV equation, we get the compact and bounded aborting set and prove the existence of the attractor for the two-dimensional weakly damped KdV equation in belt field. 相似文献
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It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1] and [2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa-Holm equation [4], we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries. 相似文献
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Wenguang Cheng Deqin Qiu Tianzhou Xu 《Mathematical Methods in the Applied Sciences》2020,43(3):1253-1266
This paper is concerned with the nth Bäcklund transformation (BT) related to multiple residual symmetries and soliton-cnoidal wave interaction solution for the combined modified KdV–negative-order modified KdV (mKdV-nmKdV) equation. The residual symmetry derived from the truncated Painlevé expansion can be extended to the multiple residual symmetries, which can be localized to Lie point symmetries by prolonging the combined mKdV-nmKdV equation to a larger system. The corresponding finite symmetry transformation, ie, nth BT, is presented in determinant form. As a result, new multiple singular soliton solutions can be obtained from known ones. We prove that the combined mKdV-nmKdV equation is integrable, possessing the second-order Lax pair and consistent Riccati expansion (CRE) property. Furthermore, we derive the exact soliton and soliton-cnoidal wave interaction solutions by applying the nonauto-BT obtained from the CRE method. 相似文献