共查询到20条相似文献,搜索用时 15 毫秒
1.
In the present study, we apply function transformation methods to the D-dimensional nonlinear Schrödinger (NLS) equation with damping and diffusive terms. As special cases, this method applies to the sine-Gordon, sinh-Gordon, and other equations. Also, the results show that these equations depend on only one function that can be obtained analytically by solving an ordinary differential equation. Furthermore, certain exact solutions of these three equations are shown to lead to the exact soliton solutions of a D-dimensional NLS equation with damping and diffusive terms. Finally, our results imply that the planar solitons, N multiple solitons, propagational breathers, and quadric solitons are solutions to the sine-Gordon, sinh-Gordon, and D-dimensional NLS equations. 相似文献
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General soliton solutions to a reverse-time nonlocal nonlinear Schrödinger (NLS) equation are discussed via a matrix version of binary Darboux transformation. With this technique, searching for solutions of the Lax pair is transferred to find vector solutions of the associated linear differential equation system. From vanishing and nonvanishing seed solutions, general vector solutions of such linear differential equation system in terms of the canonical forms of the spectral matrix can be constructed by means of triangular Toeplitz matrices. Several explicit one-soliton solutions and two-soliton solutions are provided corresponding to different forms of the spectral matrix. Furthermore, dynamics and interactions of bright solitons, degenerate solitons, breathers, rogue waves, and dark solitons are also explored graphically. 相似文献
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Theoretical and Mathematical Physics - The inverse spectral problem method is used to integrate the nonlinear Schrödinger equation with some additional terms in the class of infinite-gap... 相似文献
4.
L. Kavitha N. Akila A. Prabhu O. Kuzmanovska-Barandovska D. Gopi 《Mathematical and Computer Modelling》2011,53(5-6):1095-1110
We employed both tanh and sine–cosine function methods to study the inhomogeneous modified nonlinear Schrödinger (IMNLS) equation and constructed its exact solitary solutions by using symbolic computation software. We compared the solutions obtained by both the methods. 相似文献
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Under investigation in this paper is the integrability and dark soliton solutions for a fifth-order variable coefficients nonlinear Schrödinger equation, which is used in an inhomogeneous optical fiber. Bilinear forms, Lax pair and infinitely-many conservation laws are obtained under an integrable constraint. Dark one-, two- and N-soliton solutions are constructed via the Hirota bilinear method. 相似文献
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Th. Bartsch 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2000,17(1):366-384
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Theoretical and Mathematical Physics - We systematically present an inverse scattering transform for a nonlocal reverse-space higher-order nonlinear Schrödinger equation with nonzero boundary... 相似文献
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R. N. Garifullin 《Proceedings of the Steklov Institute of Mathematics》2013,281(1):59-63
The action of an external parametric perturbation with slowly changing frequency on a soliton of the nonlinear Schrödinger equation is studied. Equations for the time evolution of the parameters of the perturbed soliton are derived. Conditions for the soliton phase locking are found, which relate the rate of change of the perturbation frequency, its amplitude, the wave number, and the phase to the initial data of the soliton. The cases when the initial amplitude of the soliton is small and when the amplitude of the soliton is of the order of unity are considered. 相似文献
10.
We consider the multiple existence of positive solutions of the following nonlinear Schrödinger equation: where if N3 and p(1, ) if N=1,2, and a(x), b(x) are continuous functions. We assume that a(x) is nonnegative and has a potential well := int a–1(0) consisting of k components and the first eigenvalues of –+b(x) on j under Dirichlet boundary condition are positive for all . Under these conditions we show that (PM) has at least 2k–1 positive solutions for large . More precisely we show that for any given non-empty subset , (P) has a positive solutions u(x) for large . In addition for any sequence n we can extract a subsequence ni along which uni converges strongly in H1(RN). Moreover the limit function u(x)=limiuni satisfies (i) For jJ the restriction u|j of u(x) to j is a least energy solution of –v+b(x)v=vp in j and v=0 on j. (ii) u(x)=0 for .Mathematics Subject Classifications (2000):35Q55, 35J20 相似文献
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We combine the F-expansion method with the homogeneous balance principle to build a strategy to find analytical solitonic and periodic wave solutions to a generalized nonlinear Schrödinger equation with distributed coefficients, linear gain/loss, and nonlinear gain/absorption. In the case of a dimensionless effective Gross–Pitaevskii equation which describes the evolution of the wave function of a quasi-one-dimensional cigar-shaped Bose–Einstein condensate, the building strategy is applied to generate analytical solutions. 相似文献
13.
Using Morse theory, truncation arguments and an abstract critical point theorem, we obtain the existence of at least three or infinitely many nontrivial solutions for the following quasilinear Schrödinger equation in a bounded smooth domain Our main results can be viewed as a partial extension of the results of Zhang et al. in [28] and Zhou and Wu in [29] concerning the the existence of solutions to (0.1) in the case of p = 2 and a recent result of Liu and Zhao in [21] two solutions are obtained for problem 0.1.
相似文献
$$\left\{ {\begin{array}{*{20}{c}} { - {\Delta _p}u - \frac{p}{{{2^{p - 1}}}}u{\Delta _p}\left( {{u^2}} \right) = f\left( {x,u} \right)\;in\;\Omega } \\ {u = 0\;on\;\partial \Omega .} \end{array}} \right.$$
(0.1)
14.
Mónica Clapp Yanheng Ding 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,25(2):592-605
We study the nonlinear Schröodinger equation
-Du+la(x)u=mu+u2*-1, u ? \mathbbRN,-\Delta u+\lambda a(x)u=\mu u+u^{2^{\ast }-1},{ \ }u\in \mathbb{R}^{N},
with critical exponent
2*= 2
N/(
N-2),
N 4,
where
a 0,
has a potential well. Using variational methods we
establish existence and multiplicity of positive solutions which
localize near the potential well for small and
large. 相似文献
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Xiu-Fang Ren 《中国科学 数学(英文版)》2010,53(12):3067-3084
In this paper, one-dimensional (1D) nonlinear Schrdinger equation iut-uxx + Mσ u + f ( | u | 2 )u = 0, t, x ∈ R , subject to periodic boundary conditions is considered, where the nonlinearity f is a real analytic function near u = 0 with f (0) = 0, f (0) = 0, and the Floquet multiplier Mσ is defined as Mσe inx = σne inx , with σn = σ, when n 0, otherwise, σn = 0. It is proved that for each given 0 σ 1, and each given integer b 1, the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with b-dimensional Diophantine frequencies, corresponding to b-dimensional invariant tori of an associated infinite-dimensional Hamiltonian system. Moreover, these b-dimensional Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method. 相似文献
17.
NIGAR YILDIRIM AKSOY BUNYAMIN YILDIZ HAKAN YETISKIN 《Proceedings Mathematical Sciences》2012,122(3):469-484
An optimal control problem governed by a nonlinear Schr?dinger equation with complex coefficient is investigated. The paper studies existence, uniqueness and optimality conditions for the control problem. 相似文献
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P. Gaillard 《Theoretical and Mathematical Physics》2016,189(1):1440-1449
Based on a representation in terms of determinants of the order 2N, we attempt to classify quasirational solutions of the one-dimensional focusing nonlinear Schrödinger equation and also formulate several conjectures about the structure of the solutions. These solutions can be written as a product of a t-dependent exponential times a quotient of two N(N+1)th degree polynomials in x and t depending on 2N?2 parameters. It is remarkable that if all parameters are equal to zero in this representation, then we recover the PN breathers. 相似文献