共查询到20条相似文献,搜索用时 15 毫秒
1.
Polykarpos Porfyrakis Nikolaos L. Tsitsas Dimitri J. Frantzeskakis 《Mathematical Methods in the Applied Sciences》2019,42(18):7326-7334
A nonlinear (Kerr‐type) electromagnetic metamaterial, characterized by a double‐Lorentz model of its frequency‐dependent linear effective dielectric permittivity and magnetic permeability, is considered. The formation of gap solitons in the low‐ and high‐frequency band gaps of this metamaterial is investigated analytically. Evolution equations governing the gap solitons, of the form of a nonlinear Klein‐Gordon and a nonlinear Schrödinger equation, are obtained, and the structure of their solutions is discussed. 相似文献
2.
Abdul‐Majid Wazwaz 《Numerical Methods for Partial Differential Equations》2007,23(2):247-255
In this work, the sine‐cosine method, the tanh method, and specific schemes that involve hyperbolic functions are used to study solitons and periodic solutions governed by the generalized KdV equation. New solutions are determined by using the hyperbolic functions schemes. The study introduces new approaches to handle nonlinear PDEs in the solitary wave theory. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 247–255, 2007 相似文献
3.
ZHOU Zhan YU JianShe & CHEN YuMing School of Mathematics Information Science Guangzhou University Guangzhou China 《中国科学 数学(英文版)》2011,(1)
In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases. 相似文献
4.
Chengchun Hao Ling Hsiao Hai‐Liang Li 《Mathematical Methods in the Applied Sciences》2008,31(6):655-664
In this paper, we establish the global well posedness of the Cauchy problem for the Gross–Pitaevskii equation with a rotational angular momentum term in the space ?2. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations 下载免费PDF全文
We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
Gennadiy Burlak Ricardo Monroy‐Villa 《Mathematical Methods in the Applied Sciences》2019,42(15):4971-4980
We apply the variational approximation to study the dynamics of solitary waves of the nonlinear Schrödinger equation with compensative cubic‐quintic nonlinearity for asymmetric 2‐dimension setup. Such an approach allows to study the behavior of the solitons trapped in quasisymmetric potentials without an axial symmetry. Our analytical consideration allows finding the soliton profiles that are stable in a quasisymmetric geometry. We show that small perturbations of such states lead to generation of the oscillatory‐bounded solutions having 2 independent eigenfrequencies relating to the quintic nonlinear parameter. The behavior of solutions with large amplitudes is studied numerically. The resonant case when the frequency of the time variations (time managed) potential is near of the eigenfrequencies is studied too. In a resonant situation, the solitons acquire a weak time decay. 相似文献
7.
Yuen-Cheng Kuo Shih-Feng Shieh 《Journal of Mathematical Analysis and Applications》2008,347(2):521-533
In this paper, we analyze phase separation of multi-component Bose–Einstein condensates (BECs) in the presence of strong optical lattices. This paper is in threefold. We first prove that when the inter-component scattering lengths go to infinity, phase separation of a multi-component BEC occurs. Furthermore, particles repel each other and form segregated nodal domains. Secondly, we show that the union of these segregated nodal domains equal to the entire domain. Thirdly, we show that if the intra-component scattering lengths are bounded by some finite number, each nodal domain is connected. For large intra-component scattering lengths, however, the third result is not true and a counter example of non-connected nodal domains is given. 相似文献
8.
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schrödinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier–Bloch decomposition and the implicit function theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a nondegeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross–Pitaevskii equation approximated by solutions of the coupled-mode equations are obtained for a finite-time interval. 相似文献
9.
In this paper, we discuss how to use the critical point theory to study the existence of gap solitons for periodic discrete nonlinear Schrödinger equations. An open problem proposed by Professor Alexander Pankov is solved. 相似文献
10.
Alexey Slunyaev 《Studies in Applied Mathematics》2019,142(3):385-413
Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long‐wave models, the classic and the modified Korteweg–de Vries equations. The local solution for an isolated soliton or breather within the GE is obtained. The wave amplitude in the focal point is calculated exactly. It exhibits a linear superposition of partial amplitudes of the solitons and breathers. The crucial role of the choice of proper soliton polarities and breather phases on the cumulative wave amplitude in the focal point is demonstrated. Solitons are most synchronized when they have alternating polarities. The straightforward link to the problem of synchronization of envelope solitons and breathers in the focusing nonlinear Schrödinger equation is discussed (then breathers correspond to envelope solitons propagating above a condensate). 相似文献
11.
Paolo Luzzini 《Mathematical Methods in the Applied Sciences》2020,43(8):5273-5294
We introduce space-periodic layer heat potentials and we prove some regularizing properties in parabolic Schauder spaces defined on the boundary of infinite parabolic cylinders. Then, we show how to exploit these mapping properties for the space-periodic layer potentials in order to solve two initial-boundary value problems for the heat equation in an unbounded periodic domain. 相似文献
12.
In this paper, by using critical point theory in combination with periodic approximations, we obtain some new sufficient conditions on the nonexistence and existence of homoclinic solutions for a class of periodic difference equations. Unlike the existing literatures that always assume that the nonlinear terms are only either superlinear or asymptotically linear at , but superlinear at 0, our nonlinear term can mix superlinear nonlinearities with asymptotically linear ones at both and 0. To the best of our knowledge, this is the first time to consider the homoclinic solutions of this class of difference equations with mixed nonlinearities. Our results are necessary in some sense, and extend and improve some existing ones even for some special cases. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
Tomoyuki Nakatsuka 《Mathematische Nachrichten》2021,294(1):98-117
We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution of the Navier–Stokes equation such that and uniformly in as . Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described. 相似文献
14.
15.
Abdullahi Rashid Adem Chaudry Masood Khalique Anjan Biswas 《Mathematical Methods in the Applied Sciences》2011,34(5):532-543
This paper studies the solution of the Kadomtsev–Petviasvili equation with power law nonlinearity in 1+3 dimensions. The Lie symmetry approach as well as the extended tanh‐function and G′/G methods are used to carry out the analysis. Subsequently, the soliton solution is obtained for this equation with power law nonlinearity. Both topological as well as non‐topological solitons are obtained for this equation. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
16.
By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with state dependent delays where (i,j=1,2,…,n) are ω-periodic functions and (i=1,2,…,n) are ω-periodic functions with respect to their first arguments, respectively. 相似文献
17.
Grgoire Nadin 《Journal de Mathématiques Pures et Appliquées》2009,92(3):232-262
This paper is concerned with the existence of pulsating traveling fronts for the equation:(1)
∂tu−(A(t,x)u)+q(t,x)u=f(t,x,u),