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Based on some known facts of integrable models, this paper proposes a new (2+1)-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied 相似文献
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In this paper, Lie point symmetries of a new(2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple. Then, the one-dimensional optimal system,associated with corresponding Lie algebra, is obtained. Moreover, the reduction equations and some explicit solutions based on the optimal system are presented. Finally, the nonlinear selfadjointness is provided and conservation laws of this KdV system are constructed. 相似文献
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In this paper, we obtain a supersymmetric generalization for the
classical Boussinesq equation. We show that the supersymmetric
equation system passes the Painlev\'{e test and we also calculate
its one- and two-soliton solutions. 相似文献
5.
In this paper, we obtain a supersymmetric generalization for the
classical Boussinesq equation. We show that the supersymmetric
equation system passes the Painlev\'{e test and we also calculate
its one- and two-soliton solutions. 相似文献
6.
借助于符号计算软件Maple,对方程的种子解作适当的未知函数替换,然后利用Backlund 变 换通过具体的符号演算获得了(2+1)维Boussinesq方程的一系列精确解.这些解包括类孤子解 和有理解,其中有的解中含有任意函数,当任意函数取特殊函数时,这些解具有丰富的结构 ,有些结构可能对物理现象的研究是有意义的.
关键词:
(2+1)维Boussinesq方程
Backlund 变换
精确解
类孤子解 相似文献
7.
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
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MA Hong-Cai 《理论物理通讯》2005,43(6):1047-1052
Using the (2+1)-dimensional Broer-Kaup equation as an
simple example, a new direct method is developed to find symmetry
groups and symmetry algebras and then exact solutions of nonlinear
mathematical physical equations. 相似文献
9.
Finite symmetry transformation group of the Konopelchenko-Dubrovsky equation from its Lax pair
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Starting from a weak Lax pair,the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method.And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type.Furthermore,a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution. 相似文献
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Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation
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In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found. 相似文献
11.
Finite symmetry transformation group of the Konopelchenkoben Dubrovsky equation from its Lax pair
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Starting from a weak Lax pair, the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method. And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type. Furthermore, a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution. 相似文献
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A supersymmetric integrable equation in (2+1) dimensions is constructed by means of the approach of the homogenous space of the super Lie algebra, where the super Lie algebra osp(3/2) is considered. For this (2+1) dimensional integrable equation, we also derive its Bäcklund transformation. 相似文献
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利用Hirota方法及Riemann theta函数得到了(2+1)维Boussinesq方程的新的周期解.在极限情况下,该周期解退化为孤子解.
关键词:
Hirota方法
Riemann theta 函数
(2+1)维Boussinesq方程
周期解 相似文献
15.
MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(12)
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik-Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only special cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
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MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(6):1005-1010
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
17.
Junchao Chen 《Journal of Nonlinear Mathematical Physics》2014,21(3):454-472
In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials, the prolongation is found to localize the given nonlocal symmetry. Various finite-and infinite-dimensional integrable models are constructed by using the nonlocal symmetry constraint method. Moreover, applying the general Lie symmetry approach to the enlarged system, the finite symmetry transformation and similarity reductions are computed to give novel exact interaction solutions. In particular, the explicit soliton-cnoidal wave solution is obtained for the modified generalized long dispersive wave system, and it can be reduced to the two-dark-soliton solution in one special case. 相似文献
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Xi-zhong Liu 《中国物理 B》2022,31(5):50201-050201
A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method. 相似文献