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A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 相似文献
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《中国物理 B》2019,(10)
We give the bilinear form and n-soliton solutions of a(2+1)-dimensional [(2+1)-D] extended shallow water wave(eSWW) equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ(y), which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity(3k_1~2+ α, 0) on(x, y)-plane. If φ(y) = sn(y, 3/10), it is a periodic solution. If φ(y) = cn(y, 1), it is a dormion-type-Ⅰ solutions which has a maximum(3/4)k_1p_1 and a minimum-(3/4)k_1p_1. The width of the contour line is ln■. If φ(y) = sn(y, 1), we get a dormion-type-Ⅱ solution(26) which has only one extreme value-(3/2)k_1p_1. The width of the contour line is ln■. If φ(y) = sn(y, 1/2)/(1 + y~2), we get a dormion-type-Ⅲ solution(21) which shows very strong doubly localized feature on(x, y) plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way. 相似文献
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借助Mathematica符号计算软件,利用拓展的F/G展开法和变量分离法,得到(2+1)维耗散长波方程的精确解.通过选择适当的函数,获得(2+1)维耗散长波方程的亮暗dromion解和周期孤波解. 相似文献
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In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using the modified symbolic computation approach. Dynamics features of these obtained multiple rogue wave solutions are displayed in 3D and contour plots. Compared with the original symbolic computation approach, our method does not need to find Hirota bilinear form of nonlinear system. 相似文献
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Based on a special transformation that we introduce, the N-soliton solution of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular, by choosing appropriate parameters involved in the N-solitons, two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution. Five solutions including two breathers, two lumps, and interaction solutions between one breather and two bell-shaped solitons, one breather and one lump, or one lump and two bell-shaped solitons are constructed from the 4-soliton solution. Five interaction solutions mixed by one breather/lump and three bell-shaped solitons, two breathers/lumps and a bell-shaped soliton, as well as mixing with one lump, one breather and a bell-shaped soliton are constructed from the 5-soliton solution. To study the behaviors that the obtained interaction solutions may have, we present some illustrative numerical simulations, which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties. The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations. The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations. 相似文献
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In this pager a pure algebraic method implemented in a computer
algebraic system, named multiple Riccati equations rational
expansion method, is presented to construct a novel class of
complexiton solutions to integrable equations and nonintegrable
equations. By solving the (2+1)-dimensional dispersive long wave
equation, it obtains many new types of complexiton solutions such as
various combination of trigonometric periodic and hyperbolic
function solutions, various combination of trigonometric periodic
and rational function solutions, various combination of hyperbolic
and rational function solutions, etc. 相似文献
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《Waves in Random and Complex Media》2013,23(4):444-457
In this paper, a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation is investigated, which can be used to describe the interaction of a Riemann wave propagating along y-axis and a long wave propagating along x-axis. The complete integrability of the gBK equation is systematically presented. By employing Bell’s polynomials, a lucid and systematic approach is proposed to systematically study its bilinear formalism, bilinear Bäcklund transformations, Lax pairs, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic wave solutions and soliton solutions of the gBK equation are derived. Finally, an asymptotic relation between the periodic wave solutions and soliton solutions are strictly established under a certain limit condition. 相似文献
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In this paper, we propose a combined form of the bilinear Kadomtsev–Petviashvili equation and the bilinear extended(2+1)-dimensional shallow water wave equation, which is linked with a novel(2+1)-dimensional nonlinear model. This model might be applied to describe the evolution of nonlinear waves in the ocean. Under the effect of a novel combination of nonlinearity and dispersion terms, two cases of lump solutions to the(2+1)-dimensional nonlinear model are derived by searching for the quadratic... 相似文献
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New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 相似文献
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This paper investigates exact models for spherically symmetric anisotropic matter distribution in 2+1-dimensions via gravitational decoupling approach. For this purpose, we choose known spherical solutions with perfect fluid in the absence as well as the presence of cosmological constant and extend them to anisotropic models by imposing a constraint on matter components. The physical viability and stability of our developed solutions are investigated through graphical analysis of density, radial/tangential pressure, energy conditions, and causality criterion. It is found that both solutions are stable and satisfy all the physical requirements for the feasible choice of the model parameters. 相似文献
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In this paper, a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation are investigated. The first-order, second-order and third-order rogue wave solutions of this equation are derived based on a symbolic computation approach. Their dynamics features are shown in some 3D and contour plots. Compared with the previous literatures, our work does not require the Hirota bilinear form of the equation. 相似文献
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We extend the (1+1)-dimensioanl Sharma-Tasso-Olver (STO) equation to a (2+1)-dimensional one by adding one additional term uyy. A tri-linear form of the (2+1)-dimensional STO equation is obtained by the Painlevé analysis. A family of rational solutions for the (2+1)-dimensional STO equation is constructed by using the resulting tri-linear form. Associated 3-dimensional plot and density plot with particular choices of the involved parameters are given to show the charateristics of the rational solutions. 相似文献