Results 91 to 100 of about 864 (203)
Hyperbolicity versus weak periodic orbits inside homoclinic classes
, 2017 We prove that, for$C^{1}$-generic diffeomorphisms, if the periodic orbits contained in a homoclinic class$H(p)$have all their Lyapunov exponents bounded away from zero, then$H(p)$must be (uniformly) hyperbolic.
XIAODONG WANG
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, 2020 In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system.
Nikolay V. Kuznetsov +7 more
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Internal perturbations of homoclinic classes:non-domination, cycles, and self-replication
, 2010 42 pages, 1 figureConditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied.
Crovisier, S. +3 more
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Abstract and Applied Analysis, 2012 A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained ...
Defang Ma, Zhan Zhou
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
wiley +1 more source
Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Electronic Journal of Differential Equations, 2015 We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Dong-Lun Wu, Shiqing Zhang
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Harmonic Balance for Non-Periodic Hyperbolic Solutions of Nonlinear Ordinary Differential Equations
Mathematical Modelling and Analysis, 2017 In this paper, we propose a new approach for obtaining explicit analytical approximations to the homoclinic or heteroclinic solutions of a general class of strongly nonlinear ordinary differential equations describing conservative singledegree-of-freedom
Serge Bruno Yamgoue +2 more
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Homoclinics and Heteroclinics for a Class of Conservative Singular Hamiltonian Systems
Journal of Differential Equations, 1997 The authors investigate by variational methods an autonomous Hamiltonian system where the potential has a strict global maximum and a singularity at some point. They prove the existence of homoclinics which turn \(k\) times around the singularity and infinitely many geometrically distinct homoclinics. Moreover, the existence of a heteroclinic orbit and
Caldiroli, Paolo, Jeanjean, Louis
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Complexity, Volume 2025, Issue 1, 2025.The aim of this work is to study the alumina–tantalum/motor oil hybrid nanoliquid flow in a porous cavity subjected to a uniform magnetic field. We have used the Darcy–Bénard convection model for the momentum equation and a new local thermal nonequilibrium formulation for heat transport.
Sèmako Justin Dèdèwanou +9 more
wiley +1 more source
A global investigation of solitary-wave solutions to a two-parameter model for water waves
, 1996 The model equation (2r''''/15)-(br'')+(ar)+(3r^2/2)-((r')^2/2)+[rr']'=0 arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravitycapillary water waves.
Groves, MD, Champneys, AR
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