Results 1 to 10 of about 639 (179)
Homoclinic solutions for linear and linearizable ordinary differential equations
Abstract and Applied Analysis, 2000 Using functional arguments, some existence results for the infinite boundary value problem x˙=F(t,x),x(−∞)=x(+∞) are given. A solution of this problem is frequently called, from Poincaré, homoclinic.
Cezar Avramescu, Cristian Vladimirescu
doaj +5 more sources
Homoclinic Solutions for Fourth Order Traveling Wave Equations [PDF]
SIAM Journal on Mathematical Analysis, 2009 We consider homoclinic solutions of fourth order equations $$ u^{""} + β^2 u^{"} + V_u (u)=0 {in} \R ,$$ 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} $ β\in (0, β_*)$ where $ β_{*}= 0 ...
Juncheng Wei, Sanjiban Santra
exaly +3 more sources
Homoclinic and quasi-homoclinic solutions for damped differential equations
Electronic Journal of Differential Equations, 2015 We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t,u)=0, $$ where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on
Chuan-Fang Zhang, Zhi-Qing Han
doaj +2 more sources
Mathematics, 2021 The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine ...
Yanli Chen, Lei Wang, Xiaosong Yang
doaj +1 more source
Global Continuation of Homoclinic Solutions [PDF]
Zeitschrift für Analysis und ihre Anwendungen, 2018 When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under small temporally varying perturbations. In this paper, we abandon the smallness assumption and aim to investigate the global structure of the entity of all such bounded entire
Potzsche, Christian, Skiba, Robert
openaire +2 more sources
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We obtain an existence theorem of nonzero solution for a class of bounded selfadjoint operator equations. The main result contains as a special case the existence result of a nontrivial homoclinic orbit of a class of Hamiltonian systems by Coti Zelati ...
Mingliang Song, Runzhen Li
doaj +1 more source
Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach. For the case where the nonlinearity is odd, we obtain infinitely many homoclinic solutions of the equations. Recent results in the literature are generalized and improved.
Mai, Ali, Zhou, Zhan
openaire +3 more sources
Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R. Osborne
doaj +1 more source
New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation
Abstract and Applied Analysis, 2014 A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and ...
Changfu Liu +3 more
doaj +1 more source
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Shock and Vibration, 2016 The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen +2 more
doaj +1 more source