Results 101 to 110 of about 2,741,766 (204)
Convergent Analytic Solutions for Homoclinic Orbits in Reversible and Non-Reversible Systems
, 2013 In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important nonlinear
Roy Choudhury, S. +3 more
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Electronic Journal of Differential Equations, 2015 In this article, we sutdy the multiplicity of homoclinic solutions to the perturbed second-order discrete Hamiltonian system $$ \Delta[p(n)\Delta u(n-1)]-L(n)u(n)+\nabla W(n,u(n))+\theta\nabla F(n,u(n))=0, $$ where L(n) and W(n,x) are neither ...
Liang Zhang, Xianhua Tang
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Existence of homoclinic solutions for Hamiltonian systems
Advances in Differential Equations, 2002 Using variational methods, the existence of homoclinic solutions is shown for the Hamiltonian system \(Ju'(x)+Mu(x)-\nabla_uF(x,u(x))=\lambda u(x)\), where \(u : \mathbb{R}\to \mathbb{R}^{2N}\), \(J\), \(M\) are matrices such that \(J=-J^T=-J^{-1}\), \(M^T=M\) and \(F\) is a Carathéodory nonlinearity satisfying addition properties.
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Partial Differential Equations in Applied MathematicsIn this work, we develop multi-wave, homoclinic breathers, M-shaped rational, 1-kink interactions with M-shaped, periodic-cross rational and kink-cross rational solutions for the fifth-order Sawada-Kotera equation, which represents the motion of long ...
Sajawal Abbas Baloch +4 more
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The Existence of Transverse Homoclinic Solutions for Higher Order Equations
Journal of Differential Equations, 1996 Parametrized differential equations of the form \(\dot x(t)=f(x(t),\mu,t)\), where \(x\in \mathbb{R}^n\), \(\mu\in \mathbb{R}^N\), are considered. It is assumed that \(f\) is of \(C^3\)-class, \(f(x,0,t)\) is independent of \(t\), for all sufficiently small \(|\mu|\), \(x=0\) is a hyperbolic equilibrium, \(f\) is periodic in \(t\), and there exists a ...
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Homoclinic orbit solutions of a one Dimensional Wilson-Cowan type model
Electronic Journal of Differential Equations, 2008 We analyze a time independent integral equation defined on a spatially extended domain which arises in the modelling of neuronal networks. In this paper, the coupling function is oscillatory and the firing rate is a smooth "heaviside-like" function ...
Edward P. Krisner
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Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
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Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. [PDF]
ScientificWorldJournal, 2014 Sun G, Mai A.
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Homoclinic solutions in periodic partial difference equations
Advances in Nonlinear AnalysisBy using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
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Numerical analysis of the method of freezing traveling waves [PDF]
, 2005 Thümmler V. Numerical analysis of the method of freezing traveling waves. Bielefeld (Germany): Bielefeld University; 2005.In der vorliegenden Arbeit werden spezielle Lösungen von parabolischen partiellen Differentialgleichungen (PDE) u_t = A u_xx + f(u ...
Thümmler, Vera
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