共查询到20条相似文献,搜索用时 31 毫秒
1.
本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论. 相似文献
2.
This paper studies multi-solitons of non-integrable generalized Davey-Stewartson system in the elliptic-elliptic case. By extending the method for constructing multi-solitons of non-integrable nonlinear Schr¨odinger equations and systems developed by Martel et al. to the present non-integrable generalized DaveyStewartson system and overcoming some new difficulties caused by the nonlocal operator B, we prove the existence of multi-solitons for this system. Furthermore, we also give a generalization of this result to a more general class of equations with nonlocal nonlinearities. 相似文献
3.
J. Golenia O. Ye. Hentosh A. K. Prykarpatsky 《Central European Journal of Mathematics》2007,5(1):84-104
The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied. 相似文献
4.
根据基态的特征,用势井方法和凹方法证明了三维空间中广义Davey-Stewartson 系统解爆破和整体存在的最佳条件.同时还证明了当初值为多小时,该系统的整体解存在 相似文献
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(12):1427-1432
In this paper, we introduce a new numerical scheme for the nonlinear Schrödinger equation and the Davey-Stewartson systems. This is a relaxation type scheme that avoids the resolution of nonlinear systems. We give convergence results for the semi-discret version, locally in time for all data and globally in time for small data. 相似文献
6.
Cheng-chun HaoAcademy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2003,19(2):333-340
Abstract Considring the generalized Davey-Stewartson equation i-△u+λ│u│~pu+μE(│u│~q)│u│~(q-2)u=0,where λ>0,μ≥0,E=F~(-1)(ξ_1~2│ξ│~2)F,we obtain the existence of scattering operator in ∑(R~n):u{u∈H~1(R~n):│x│u∈L~2(R~n)}. 相似文献
7.
8.
《数学物理学报(B辑英文版)》2020,(4)
In this paper, we give a simpler proof for Ohta's theorems [1995, Ann. Inst.Henri Poincare, 63, 111; 1995, Diff. Integral Eq., 8, 1775] on the strong instability of the ground states for a generalized Davey-Stewartson system. In addition, a sufficient condition is given to ensure the nonexistence of a minimizer for a variational problem, which is related to the stability of the standing waves of the Davey-Stewartson system. This result shows that the stability result of Ohta [Diff. Integral Eq., 8, 1775] is sharp. 相似文献
9.
By the variable transformation and generalized Hirota method, exact homoclinic and heteroclinic solutions for Davey-Stewartson II (DSII) equation are obtained. For perturbed DSII equation, the existence of a global attractor is proved. The persistence of homoclinic and heteroclinic flows is investigated, and the special homoclinic and heteroclinic structure in attractors is shown. 相似文献
10.
根据基态的特征 ,首先在二维空间中导出了广义Davey Stewartson系统解爆破和整体存在的最佳条件 ;其次得到了整体解存在的一个最佳充分条件 ;最后证明了当初值为多小时 ,该系统的整体解存在 . 相似文献
11.
Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法. 相似文献
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13.
F. Pempinelli 《Theoretical and Mathematical Physics》1994,99(3):755-760
By introducing generalized Bäcklund transformations depending on arbitrary functions, wave and localized soliton solutions of the Davey-Stewartson equations are generated. Moreover, explicit soliton solutions of the Hamiltonian DSI and DSIII equations are obtained.Dipartimento di Fisica dell'Università e Sezione INFN, 73100 Lecce, Italy. E-mail: pempi@lecce.infn. it. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 501–508, June, 1994. 相似文献
14.
The differential-geometric properties of generalized de Rham-Hodge complexes naturally related with integrable multidimensional differential systems of M. Gromov type are analyzed. The geometric structure of Chern type characteristic classes are studied, special differential invariants of the Chern type are constructed. The integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
In this paper, we extend the homotopy perturbation method to solve the Davey-Stewartson equations. The homotopy perturbation
method is employed to compute an approximation to the solution of the equations. Computation the absolute errors between the
exact solutions of the Davey-Stewartson equations and the HPM solutions are presented. Some plots are given to show the simplicity
the method.
The article is published in the original. 相似文献
16.
在Banach空间中研究与时间有关的抛物型发展微分包含,这一问题与非线性分布参数控制系统的研究密切相关.我们证明了mild-解的存在性,同时研究了解集的拓扑性质.本文的研究发展和推广J.P.Aubin等人的方向和结果. 相似文献
17.
《应用数学年刊》2014,(1)
For the Davey-Stewartson system,the exact dark solitary wave solutions,solitary wave solutions,kink wave solution and periodic wave solutions are studied.To guarantee the existence of the above solutions,all parameter conditions are determined.The persistence of dark solitary wave solutions to the perturbed Davey-Stewartson system is proved. 相似文献
18.
本文研究方程驻波的强不稳定性iu_t+△u+a|u|~(p-1)u+E_1(|u|~2)u=0,t≥0,x∈R~n,其中a0,1p(n+2)/(n+2)~+,n∈{2,3}.当1+4/n≤pn+2/(n-2)~+)时,文[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system,Commun.Math.Phys.,2008,283:93-125]在驻波的频率满足一定假设条件下,证明了此方程驻波的强不稳定性.本文去掉这个假设,得到相同的结论. 相似文献
19.
The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state. 相似文献
20.
A class of multidimensional nonlinear evolution equations of physical interest are considered in the limit of strong coupling. It turns out that the initial value solution is readily obtained. In the special case of the Davey-Stewartson equation the inverse scattering transform is shown to reduce to the obtained solution via perturbation. A number of other features are discussed as well, such as action angle variables, periodic solutions, and quantum analogues. 相似文献