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1.
The new (2+1)-dimensional generalized KdV equation which exists the bilinear form is mainly discussed. We prove that the equation does not admit the Painlevé property even by taking the arbitrary constant a=0. However, this result is different from Radha and Lakshmanan??s work. In addition, based on Hirota bilinear method, periodic wave solutions in terms of Riemann theta function and rational solutions are derived, respectively. The asymptotic properties of the periodic wave solutions are analyzed in detail. 相似文献
2.
In present work, new form of generalized fifth-order nonlinear integrable equation has been investigated by locating movable critical points with aid of Painlevé analysis and it has been found that this equation passes Painlevé test for \(\alpha =\beta \) which implies affirmation toward the complete integrability. Lie symmetry analysis is implemented to obtain the infinitesimals of the group of transformations of underlying equation, which has been further pre-owned to furnish reduced ordinary differential equations. These are then used to establish new abundant exact group-invariant solutions involving various arbitrary constants in a uniform manner. 相似文献
5.
In this paper, the (2+1)-dimensional Sawada–Kotera model is studied with the Hirota bilinear method, gauge transformation and symbolic computation. Based on an alternative bilinear representation of the model, a bilinear Bäcklund transformation (BT) with three arbitrary constants is derived. Via applying a gauge transformation to this BT and choosing suitable constant parameters, three other sets of bilinear BTs are constructed, among which, the last set is treated as a new bilinear BT and denoted as BTIV hereby. Finally, by performing the perturbation technique on the new bilinear BT, namely BTIV, multisoliton solutions are iteratively achieved, and as an example, the one-, two- and three-soliton solutions are explicitly given. Note that formulas of the soliton solutions obtained hereby through solving the BTIV are different from the previous ones in other literature. 相似文献
6.
Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Bäcklund transformations of the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation starting from the specially exchange identities of the Hirota bilinear operators; then, we construct the N-soliton solutions and several new structures of the localized wave solutions which are studied by using the long wave limit method and the complex conjugate condition technique. In addition, the propagation orbit, velocity and extremum of the first-order lump solution on (x, y)-plane are studied in detail, and seven mixed solutions are summarized. Finally, the dynamical behaviors and physical properties of different localized wave solutions are illustrated and analyzed. It is hoped that the obtained results can provide a feasibility analysis for water wave dynamics. 相似文献
7.
Nonlinear Dynamics - In this paper, the truncated Painlevé expansion is employed to derive a Bäcklund transformation of a ( $$2+1$$ )-dimensional nonlinear system. This system can be... 相似文献
8.
In the following we consider a 2-dimensional system of ODEs containing quasiperiodic terms. The system is proposed as an extension
of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal frequencies leads to a
loss of stability. The 2-d system has two ‘natural’ frequencies when the time-dependent terms are switched off, and it is
internally driven by quasiperiodic terms in the same frequencies. Stability charts in the parameter space are generated first
using numerical simulations and Floquet theory. While some instability regions are easy to anticipate, there are some surprises:
within instability zones, small islands of stability develop, and unusual ‘arcs’ of instability arise also. The transition
curves are analyzed using the method of harmonic balance, and we find we can use this method to easily predict the ‘resonance
curves’ from which bands of instability emanate. In addition, the method of multiple scales is used to examine the islands
of stability near the 1:1 resonance. 相似文献
10.
Nonlinear Dynamics - Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the ( $$2+1$$... 相似文献
11.
Nonlinear Dynamics - In this paper, the generalized unified method is used to construct multi-rational wave solutions of the ( $$2 + 1$$ )-dimensional Kadomtsev–Petviashvili equation with... 相似文献
12.
We consider a Cauchy–Dirichlet problem for the isotropic Lamé system with variable coefficients. We find an estimate for the L2 -norm of the surface traction in terms of the initial data and the body force. Then we show that, in absence of body forces, the elastic energy can be controlled by the L2 -norm of the surface traction exerted on a suitable sub-boundary, provided that the time interval is sufficiently large. These inequalities are basic for the applicability of the so-called HUM (Hilbert Uniqueness Method) and they can also be used to solve an inverse source problem for the Lamé system. 相似文献
14.
In this paper, a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid is investigated. By the virtue of the truncated Painlevé expansion, a set of the auto-Bäcklund transformations of that equation is worked out. Based on the auto-Bäcklund transformations with certain non-trivial seed solutions, one-, two-, three- and N-soliton solutions on the nonzero background of that equation are derived with N as a positive integer. According to those two-soliton solutions, X- and inelastic-type soliton solutions are obtained. Via the asymptotic analysis, influence of the coefficients for the above equation is discussed and the interactions between the solitons are also studied. Then, those solitons and interactions are shown graphically.
相似文献
16.
Nonlinear Dynamics - In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund... 相似文献
17.
Nonlinear Dynamics - This paper is concerned with the variable-coefficient Gardner (vc-Gardner) types of equations, which arise in fluid dynamics, nonlinear lattice and plasma physics. As its... 相似文献
18.
In this paper, the three variable-coefficient Gardner (vc-Gardner) equations are considered. By using the Painlevé analysis
and Lie group analysis method, the Painlevé properties and symmetries for the equations are obtained. Then the exact solutions
generated from the symmetries and Painlevé analysis are presented. 相似文献
19.
In this paper, outcomes of the study on the Bäcklund transformation, Lax pair, and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, fluid mechanics, and plasma physics are presented. Via the Hirota bilinear method, a bilinear Bäcklund transformation is obtained, based on which a Lax pair is constructed. Via the symbolic computation, mixed rogue–solitary and rogue–periodic wave solutions are derived. Interactions between the rogue waves and solitary waves, and interactions between the rogue waves and periodic waves, are studied. It is found that (1) the one rogue wave appears between the two solitary waves and then merges with the two solitary waves; (2) the interaction between the one rogue wave and one periodic wave is periodic; and (3) the periodic lump waves with the amplitudes invariant are depicted. Furthermore, effects of the noise perturbations on the obtained solutions will be investigated. 相似文献
20.
Nonlinear Dynamics - Under investigation in this work is a $$(2+1)$$ -dimensional Davey–Stewartson system, which describes the surface water wave packets of finite depth. With respect to the... 相似文献
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