Results 31 to 40 of about 8,918 (208)
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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Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction [PDF]
, 2007 We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers.
Bernardo Sánchez-rey B +3 more
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Homoclinic Solutions for Fourth Order Traveling Wave Equations [PDF]
SIAM Journal on Mathematical Analysis, 2009 We consider homoclinic solutions of fourth order equations $$ u^{""} + ^2 u^{"} + V_u (u)=0 {in} \R ,$$ where $V(u)$ is either the suspension bridge type $V(u)=e^u-1-u$ or Swift-Hohenberg type $ V(u)= {1/4}(u^2-1)^2$. For the suspension bridge type equation, we prove existence of a homoclinic solution for {\em all} $ \in (0, _*)$ where $ _ ...
Santra, Sanjiban, Wei, Juncheng
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Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation
Abstract and Applied Analysis, 2014 A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed.
Hanlin Chen, Zhenhui Xu, Zhengde Dai
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Homoclinic Solutions of Hamiltonian Systems with Symmetry
Journal of Differential Equations, 1999 Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
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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 +30 more
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Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems
Abstract and Applied Analysis, 2013 We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
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On Existence of Infinitely Many Homoclinic Solutions
Monatshefte f�r Mathematik, 2000 Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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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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