共查询到20条相似文献,搜索用时 15 毫秒
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Yun-Hu Wang 《Mathematical Methods in the Applied Sciences》2015,38(1):138-144
Under investigation in this paper are the (1+1)-dimensional and (2+1)-dimensional Ito equations. With the help of the Bell polynomials method, Hirota bilinear method and symbolic computation, the bilinear representations, N-soliton solutions, bilinear Bäcklund transformations and Lax pairs of these two equations are obtained, respectively. In particular, we obtain a new bilinear form and N-soliton solutions of the (2+1)-dimensional Ito equation. The bilinear Bäcklund transformation and Lax pair of the (2+1)-dimensional Ito equation are also obtained for the first time. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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本文对(2+1)维变系数Broer-Kaup方程和wick型随机(2+1)维Broer-Kaup方程进行了研究,利用Hermite变换、齐次平衡法以及tanh函数法给出了wick型随机(2+1)维Broer-Kaup方程的B(a)cklund变换和白噪声泛函解. 相似文献
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Symbolic-computation study of integrable properties for the (2 + 1)-dimensional Gardner equation with the two-singular manifold method 总被引:1,自引:0,他引:1
Zhang Hai-Qiang; Tian Bo; Li Juan; Xu Tao; Zhang Ya-Xing 《IMA Journal of Applied Mathematics》2009,74(1):46-61
The singular manifold method from the Painlevé analysiscan be used to investigate many important integrable propertiesfor the non-linear partial differential equations. In this paper,the two-singular manifold method is applied to the (2 + 1)-dimensionalGardner equation with two Painlevé expansion branchesto determine the Hirota bilinear form, Bäcklund transformation,Lax pairs and Darboux transformation. Based on the obtainedLax pairs, the binary Darboux transformation is constructedand the N x N Grammian solution is also derived by performingthe iterative algorithm N times with symbolic computation. 相似文献
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M. Yu. Balakhnev 《Mathematical Notes》2007,82(3-4):448-450
Using the Bäcklund transformations, we obtain superposition formulas for vector generalizations of the mKdV equation. 相似文献
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A Bäcklund transformation (BT), which involves both independent and dependent variables, is established and studied for the short pulse (SP) equation. Based it, the nonlinear superposition formulae for 2-, 3-, and 4-BT are presented. The general result for the composition of -BTs is achieved and given in terms of determinants. As applications, various solutions including loop solitons, breather solutions, and their interaction solutions are worked out. 相似文献
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We directly construct a bilinear Bäcklund transformation (BT) of a (2+1)-dimensional Korteweg–de Vries-like model. The construction is based on a so-called quadrilinear representation. The resulting bilinear BT is in accordance with the auxiliary-independent-variable-involved one derived with the Bell-polynomial scheme. Moreover, by applying the gauge transformation and the Hirota perturbation technique, multisoliton solutions are iteratively computed. 相似文献
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Zhenya YAN Institute of Mathematical Science Dalian University of Technology Dalian China e-mail: zhanghq@dlut. edu.cn 《Communications in Nonlinear Science & Numerical Simulation》2000,(1)
IntroductionDuring the study of water wave, many completely iategrable models were derived, such as(1+1)-dimensional KdV equation, MKdV equation, (2+1)-dimensional KdV equation, Boussinesq equation and WBK equations etc. Many properties of these models had been researched,such as BAcklund transformation (BT), converse rules, N-soliton solutions and Painleve property etc.II--8]. In this paper, we would like to consider (2+1)-dimensional variable coefficientgeneralized KP equation which … 相似文献
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In this paper, the (2 + 1)-dimensional Korteweg-de Vries system is symbolically investigated. By the bilinear method, the N-soliton solution is presented. Then, based on the Bäcklund transformation in bilinear form, a new Bäcklund transformation is obtained and new representation of the N-soliton solution is derived. A class of novel multi-soliton solutions are obtained by the new Bäcklund transformation and the availability of symbolic computation is demonstrated. 相似文献
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In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed. 相似文献
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A 2 + 1-dimensional Volttera type lattice is proposed. Resorting to the nonlinearization of Lax pair, the 2 + 1-dimensional Volttera type lattice is decomposed into the known 1+1-dimensional differential-difference equations. The relation between a new 2 + 1-dimensional differential-difference equation, certain 1+1-dimensional continuous evolution equations and the known 1+1-dimensional differential-difference equations is discussed. Based on finite-order expansion of the Lax matrix, we introduce elliptic coordinates, from which the two 2 + 1-dimensional differential-difference equations are separated into solvable ordinary differential equations. The evolution of various flows is explicitly given through the Abel–Jacobi coordinates. Quasi-periodic solutions for the two 2 + 1-dimensional differential-difference equations are obtained. 相似文献
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一个2+1维变形Boussinesq方程的N孤子解 总被引:1,自引:0,他引:1
研究了一个2+1维变形Boussinesq非线性发展方程:utt-uxx-uyy-3(u^2)xx-uxxxx=0,运用Hirota双线性方法得到它的N孤子解. 相似文献
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Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Bilinear form and Bäcklund transformation are derived by virtue of the Bell polynomials. Besides, the one- and two-soliton solutions are constructed via the Hirota method. 相似文献
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(2+1)维广义Burgers 方程的Lie点对称, 相似约化和精确解 总被引:2,自引:1,他引:1
讨论了(2+1)维广义Burgers方程.通过Lie群方法求出了该方程的李点对称,并利用李点对称将方程进行相似约化,求出了(2+1)维广义Burgers方程的几种精确解.该方法可以用于研究更高阶的偏微分方程. 相似文献
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A class of exact Pfaffian solutions to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation is obtained. A set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters is generated to guarantee that the Pfaffian solves the equation. A Bäcklund transformation of the equation is presented. The equation is transformed into a set of bilinear equations, and a few classes of traveling wave solutions, rational solutions and Pfaffian solutions to the extended bilinear equations are furnished. Examples of the Pfaffian solutions are explicitly computed, and a few solutions are plotted. 相似文献
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We investigate a generalized (3 + 1)-dimensional nonlinear wave equation, which can be used to depict many nonlinear phenomena in liquid containing gas bubbles. By employing the Hirota bilinear method, we derive its bilinear formalism and soliton solutions succinctly. Meanwhile, the first-order lump wave solution and second-order lump wave solution are well presented based on the corresponding two-soliton solution and four-soliton solution. Furthermore, two types of hybrid solutions are systematically established by using the long wave limit method. Finally, the graphical analyses of the obtained solutions are represented in order to better understand their dynamical behaviors. 相似文献
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A consistent Riccati expansion (CRE) is proposed to solve the (2+1)‐dimensional modified dispersive water‐wave (MDWW) system. It is proved that the MDWW system is CRE solvable. Furthermore, new exact interaction solutions, namely, soliton‐trigonometric waves, trigonometric waves‐soliton, soliton‐cosine periodic waves, and soliton‐cnoidal waves are explicitly derived. 相似文献