共查询到20条相似文献,搜索用时 171 毫秒
1.
Chuanhai Xu Yuhai Wu Lixin Tian Boling Guo 《Journal of Applied Analysis & Computation》2018,8(5):1385-1395
This paper deals with existence problem of traveling wave solutions of a class of nonlinear Schr\"{o}dinger equation having distributed delay with a strong generic kernal. By using the geometric singular perturbation theory and the Melnikov function method, we establish results of the existence of kink and anti-kink wave solutions of the nonlinear Schr\"{o}dinger equation with time delay when the average delay is sufficiently small. 相似文献
2.
Bi-solitons, breather solution family and rogue waves for the (2+1)-dimensional nonlinear Schr\"{o}dinger equation 下载免费PDF全文
Changfu Liu Min Chen Ping Zhou Longwei Chen 《Journal of Applied Analysis & Computation》2016,6(2):367-375
In this paper, bi-solitons, breather solution family and rogue
waves for the (2+1)-Dimensional nonlinear Schr\"{o}dinger equations
are obtained by using Exp-function method. These solutions derived
from one unified formula which is solution of the standard (1+1)
dimension nonlinear Schr\"{o}dinger equation. Further, based on the
solution obtained by other authors, higher-order rational rogue wave
solution are obtained by using the similarity transformation. These
results greatly enriched the diversity of wave structures for the
(2+1)-dimensional nonlinear Schr\"{o}dinger equations 相似文献
3.
In this paper, the problem of a class of multidimensional fourth-order nonlinear Schr\"{o}dinger equation including the derivatives of the unknown function in the nonlinear term is studied, and the existence of global weak solutions of nonlinear Schr\"{o}dinger equation is proved by the Galerkin method according to the different values of $\lambda$. 相似文献
4.
本文提出了一种全新复合$(\frac{G''}{G})$展开方法,运用这种新方法并借助符号计算软件构造了非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的多种双行波解,包括双双曲正切函数解,双正切函数解,双有理函数解以及它们的混合解. 复合$(\frac{G''}{G})$展开方法不但直接有效地求出了两类非线性偏微分方程的双行波解,而且扩大了解的范围.这种新方法对于研究非线性偏微分方程具有广泛的应用意义. 相似文献
5.
The new exact solutions of variant types of time fractional coupled Schr\"{o}dinger equations in plasma physics 下载免费PDF全文
In the present article, the new exact solutions of fractional coupled Schr\"{o}dinger type equations have been studied by using a new reliable analytical method. We applied a relatively new method for finding some new exact solutions of time fractional coupled equations viz. time fractional coupled Schr\"{o}dinger--KdV and coupled Schr\"{o}dinger--Boussinesq equations. The fractional complex transform have been used here along with the property of local fractional calculus for reduction of fractional partial differential equations (FPDE) to ordinary differential equations (ODE). The obtained results have been plotted here for demonstrating the nature of the solutions. 相似文献
6.
Dynamical behaviour and exact solutions of thirteenth order derivative nonlinear Schr\"{o}dinger equation 下载免费PDF全文
In this paper, we considered the model of the thirteenth order derivatives of nonlinear Schr\"{o}dinger equations. It is shown that a wave packet ansatz inserted into these equations leads to an integrable Hamiltonian dynamical sub-system. By using bifurcation theory of planar dynamical systems, in different parametric regions, we determined the phase portraits. In each of these parametric regions we obtain possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, hetroclinic and periodic orbits. 相似文献
7.
Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schr\"{o}dinger equations to discrete Hamiltonian systems. In recent years, a lot of interesting results on the homoclinic solutions of difference equations have been obtained. In this paper, we review some recent progress by using critical point theory to study the existence and multiplicity results of homoclinic solutions in some discrete nonlinear systems with variational structure. 相似文献
8.
Painlev\''{e} Analysis and Auto-B\"{a}cklund Transformation for a General Variable Coefficient Burgers Equation with Linear Damping Term 下载免费PDF全文
This paper investigates a general variable coefficient (gVC) Burgers equation with linear damping term. We derive the Painlev\''{e} property of the equation under certain constraint condition of the coefficients. Then we obtain an auto-B\"{a}cklund transformation of this equation in terms of the Painlev\''{e} property. Finally, we find a large number of new explicit exact solutions of the equation. Especially, infinite explicit exact singular wave solutions are obtained for the first time. It is worth noting that these singular wave solutions will blow up on some lines or curves in the $(x,t)$ plane. These facts reflect the complexity of the structure of the solution of the gVC Burgers equation with linear damping term. It also reflects the complexity of nonlinear wave propagation in fluid from one aspect. 相似文献
9.
10.
Generalized local Morrey spaces and multilinear commutators generated by Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators and local Campanato functions 下载免费PDF全文
Ferit Gürbüz 《Journal of Applied Analysis & Computation》2018,8(5):1369-1384
Let $L=-\Delta+V\left( x\right) $ be a Schr\"{o}dinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V\left( x\right) $ belongs to the reverse H\"{o}lder class. In this paper, we consider the behavior of multilinear commutators of Marcinkiewicz integrals with rough kernel associated with Schr\"{o}dinger operators on generalized local Morrey spaces. 相似文献
11.
Bifurcations and exact solutions of nonlinear Schrodinger equation with an anti-cubic nonlinearity 下载免费PDF全文
In this paper, we consider the nonlinear Schr\"{o}dinger equation with an anti-cubic nonlinearity. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to different level curves defined by the Hamiltonian, we derive all exact explicit parametric representations of the bounded solutions (including periodic peakon solutions, periodic solutions, homoclinic solutions, heteroclinic solutions and compacton solutions). 相似文献
12.
Divergent Solution to the Nonlinear Schr\"{o}dinger Equation with the Combined Power-Type Nonlinearities 下载免费PDF全文
In this paper, we consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation with combined power-type nonlinearities, which is mass-critical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang'' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the $H^1$-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time. 相似文献
13.
乔蕾 《数学年刊A辑(中文版)》2016,37(3):303-310
给出了锥中稳态Schr\"{o}dinger方程解的Liouville型定理,
推广了邓冠铁在半空间中关于拉普拉斯方程解的相关结论. 相似文献
14.
Local exact controllability of Schr\"{o}dinger equation with Sturm- Liouville boundary value problems 下载免费PDF全文
In this paper, we investigate the controllability of 1D bilinear Schr\"{o}dinger equation with Sturm-Liouville boundary value condition. The system represents a quantumn particle controlled by an electric field. K. Beauchard and C. Laurent have proved local controllability of 1D bilinear Schr\"{o}dinger equation with Dirichlet boundary value condition in some suitable Sobolev space based on the classical inverse mapping theorem. Using a similar method, we extend this result to Sturm-Liouville boundary value proplems. 相似文献
15.
In this paper, we investigate the Schr\"{o}dinger equation, which satisfies that the potential is asymptotical 0 at infinity in some measure-theoretic and the nonlinearity is sublinear growth. By using variant symmetric mountain lemma, we obtain infinitely many solutions for the problem. Moreover, if the nonlinearity is locally sublinear defined for $|u|$ small, we can also get the same result. In which, we show that these solutions tend to zero in $L^{\infty}(\mathbb{R}^{N})$ by the Br\"{e}zis-Kato estimate. 相似文献
16.
Summary. We examine the use of orthogonal spline collocation for the
semi-discreti\-za\-tion of the cubic Schr\"{o}dinger equation and the
two-dimensional
parabolic equation of Tappert. In each case, an optimal order
estimate of the error in the semidiscrete
approximation is derived. For the cubic Schr\"{o}dinger equation, we
present the results
of numerical experiments in which the integration in time is
performed using a routine from a software library.
Received February 14, 1992 / Revised version received December 29,
1992 相似文献
17.
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved. 相似文献
18.
In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ where $\mu,\nu\ge 0$, and $rV(r)$ is an entire function of $r=+(x^2+y^2)^{1/2}$ corresponding to a scattering potential $V(r)$. Growth parameters of entire function solutions in terms of their expansion coefficients, which are analogous to the formulas for order and type occurring in classical function theory, have been obtained. Our results are applicable for the scattering of particles in quantum mechanics. 相似文献
19.
In this paper we show that a positive superfunction on a cone behaves regularly at infinity outside a minimally thin set associated with the stationary Schr(o|¨)dinger operator. 相似文献