共查询到20条相似文献,搜索用时 15 毫秒
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Abdul-Majid Wazwaz 《Central European Journal of Physics》2011,9(3):835-840
The integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve
this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation.
The resonance phenomenon of each model will be examined. 相似文献
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ABDUL-MAJID WAZWAZ 《Pramana》2011,77(2):233-242
The integrability of two coupled KP equations is studied. The simplified Hereman form of Hirota’s bilinear method is used
to examine the integrability of each coupled equation. Multiple-soliton solutions and multiple singular soliton solutions
are formally derived for each coupled KdV equation. 相似文献
4.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,50(10):809-813
A special coupled KdV equation is proved to be the Painleve property by the Kruskal's simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota's bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically. 相似文献
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The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed. 相似文献
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CHEN Jin-Bing GENG Xian-Guo 《理论物理通讯》2005,44(9)
This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure. 相似文献
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CHEN Jin-Bing GENG Xian-Guo 《理论物理通讯》2005,44(3):393-395
This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R^2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure. 相似文献
8.
A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations
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A modified Korteweg-de Vries (mKdV) lattice is found to be also a discrete Korteweg-de Vries (KdV) equation. A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics. 相似文献
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利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波.
关键词:
cKdV方程
双扭结单孤子
稳定性 相似文献
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Painleve Integrability,Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System
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《中国物理快报》2017,(1)
The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli(mKdVBLMP) system is investigated using the Painleve analysis approach. It is shown that this coupled system possesses the Painleve property in both the principal and secondary branches. Then, the consistent Riccati expansion(CRE)method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally; starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly. 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(3):230-233
Abstract A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé; test for integrability well, and its 4×4 Lax pair with two spectral parameters is found. The results show that the Painlevé; classification of coupled KdV equations by A. Karasu should be revised. 相似文献
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Abdul-Majid Wazwaz 《Waves in Random and Complex Media》2018,28(3):533-543
A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV–nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions. 相似文献
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ZUO Da-Feng 《理论物理通讯》2010,54(6):962-964
In this paper, we propose a fermionic generalization of KdV6 equation and study its integrability. Moreover, we show that this equation is a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra. 相似文献
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A. Roy Chowdhury Pritha Mitra Sasanka Purkait 《International Journal of Theoretical Physics》1990,29(8):867-871
Painlevé analysis is performed for the coupled system of nonlinear partial differential equations consisting of the KdV equation and NLS equation initially studied by Nishikawa. Various possibilities for the constants occurring in the system are explored, paying attention to the integrability property. This equation occurring in the field of plasma physics satisfies all the requirements of Painlevé analysis and can be ascertained to be completely integrable, though no Lax pair is known for it. 相似文献
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Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation
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Sayed A. El-Wakil Essam M. Abulwaf Emad K. El-Shewy Abeer A. Mahmoud 《中国物理 B》2011,20(4):40508-040508
The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments,such as the ionosphere plasma. 相似文献
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Abdul-Majid Wazwaz 《Waves in Random and Complex Media》2020,30(2):300-307
ABSTRACTIn this work we use the repeated application of the recursion operator to establish a new hierarchy of negative-order integrable KdV equations of higher orders. The concept of the inverse recursion operator allows us to develop this new hierarchy. The complete integrability of each equation is guaranteed via the use of the recursion operator. We show that the dispersion relations of this hierarchy follow an infinite geometric series. Multiple soliton solutions for each equation of the hierarchy are obtained. 相似文献
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Abdul-Majid Wazwaz 《Waves in Random and Complex Media》2019,29(2):195-203
We develop a variety of negative-order integrable KdV equations of higher orders. We use the inverse recursion operator to construct these new equations. The complete integrability of each established equation is investigated via the Painlevé test, where each equation shows distinct branch of resonances. We use the simplified form of the Hirota’s direct method to obtain multiple soliton solutions for the generalized negative-order KdV equation. 相似文献
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《等离子体物理论文集》2017,57(5):223-232
An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated. 相似文献
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The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results. 相似文献