Results 31 to 40 of about 9,595 (205)

Multiple homoclinic solutions for a one-dimensional Schrödinger equation [PDF]

Discrete & Continuous Dynamical Systems - S, 2016
This paper is dedicated to the study of the problem of existence of homoclinic solutions to a Schrödinger equation of the form \[ x''-V(t)x+x^3=0,\eqno{(1)} \] where \(V:\mathbb R\to\mathbb R\) is a \(L^1\)-function.
DAMBROSIO, Walter, D. Papini
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On periodic orbits in a slow-fast system with normally elliptic slow manifold [PDF]

, 2013
In this note we consider the bifurcation of a singular homoclinic orbit to periodic ones in a 4-dimensional slow-fast system of ordinary differential equations, having a 2-dimensional normally elliptic slow manifold, originally studied by Feckan and ...
Sourdis, Christos
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Center Manifolds for Homoclinic Solutions

Journal of Dynamics and Differential Equations, 2000
In this article, center-manifold theory for homoclinic solutions of ordinary differential equations or semilinear parabolic equations is developed. Here, a center manifold along a homoclinic orbit q(t) is a locally invariant manifold containing all solutions which stay close to q(t) in phase space for all times. Therefore, as usual, the low-dimensional
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Homoclinic solutions for a class of non-periodic second order Hamiltonian systems

Electronic Journal of Qualitative Theory of Differential Equations, 2010
We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth ...
Jian Ding, Junxiang Xu, Fubao Zhang
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Twisted and Nontwisted Bifurcations Induced by Diffusion

, 1996
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop.
A. Lunardi, A. M. Turing, B. Deng, E. Conway, E. D. Conway, E. Yanagida, G. Prato Da, G. S. K. Wolkowicz, H. I. Freedman, H. Kokubu, J. Carr, J. D. Murray, J. K. Hale, L. P. Silnikov, P. C. Fife, P. Hartman, S.-N. Chow, S.-N. Chow, S.-N. Chow, S.-N. Chow, X. B. Lin, X. B. Lin, X. B. Lin, X.-B. Lin, X.-B. Lin, Xiao-Biao Lin   +25 more
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Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems

Abstract and Applied Analysis, 2013
This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a ...
Jingli Xie, Zhiguo Luo, Guoping Chen
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Global bifurcation of homoclinic trajectories of discrete dynamical systems [PDF]

, 2012
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological properties of the ...
A. Abbondandolo, A.G. Baskakov, C. Pötzsche, C. Pötzsche, C. Pötzsche, D. Husemoller, G. Bachman, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, J.C. Alexander, M. Rasmussen, M.F. Atiyah, P.M. Fitzpatrick, P.M. Fitzpatrick, R.J. Sacker, S. Secchi, T. Bartsch, T. Kato   +20 more
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Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

, 2013
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations.
Choudhury, S. Roy, Gambino, G., Rehman, T.   +2 more
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Global bifurcation of homoclinic solutions of Hamiltonian systems

Discrete & Continuous Dynamical Systems - A, 2003
We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
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Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization [PDF]

, 2011
We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons).
A. Khare, A. Pankov, A. Pankov, A. Pankov, A. Pankov, C. A. Stuart, D. E. Pelinovsky, D. E. Pelinovsky, G. Zhang, G. Zhang, H. Shi, J. A. Pava, J. C. Eilbeck, J. Ch. Eilbeck, J. Dorignac, J. Yang, M. A. Porter, M. Herrmann, M. I. Weinstein, M. I. Weinstein, Michael Herrmann, P. G. Kevrekidis, P. G. Kevrekidis, P. G. Kevrekidis, P. G. Kevrekidis, P.-L. Lions, R. S. MacKay, S. Aubry, S. Flach, W. Bao, W.-X. Qin   +30 more
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