Results 51 to 60 of about 8,851 (211)

Homoclinic solutions for second order Hamiltonian systems with general potentials near the origin

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
Qingye Zhang
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

Predicting rogue waves in random oceanic sea states [PDF]

, 2004
Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS equation.
Islas, Alvaro, Schober, Constance
core   +4 more sources

Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schr\"odinger Equation

, 2005
We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities.
Alfimov, Aubry, B.A. Malomed, Boudebs, Bountis, C. Chong, Campbell, Carretero-González, Carretero-González, Cataliotti, Chen, Cheskis, Christodoulides, Christodoulides, Cowan, Dauxois, Dorignac, Eisenberg, Flach, Flach, Fleischer, Gisin, Greiner, Hadžievski, J.D. Talley, Kapitula, Kevrekidis, Kevrekidis, Khare, Koukouloyannis, Koukouloyannis, Laedke, Li, MacKay, Malomed, Malomed, Merhasin, Pertsch, Porter, Pushkarov, R. Carretero-González, Sato, Sato, Seaman, Smektala, Stepić, Trombettoni, Tsironis, Tsironis, Vakhitov, Vinetskii, Wang, Zhan, Öster   +53 more
core   +1 more source

Whitham Averaged Equations and Modulational Stability of Periodic Traveling Waves of a Hyperbolic-Parabolic Balance Law [PDF]

, 2010
In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline.
Barker, Blake, Johnson, Mathew A., Noble, Pascal, Rodrigues, L. Miguel, Zumbrun, Kevin   +4 more
core   +5 more sources

A Survey of SIR‐Based Differential Epidemic Models for Control and Security Against Malware Propagation in Computer Networks

SECURITY AND PRIVACY, Volume 9, Issue 1, January/February 2026.
ABSTRACT Unarguably, malware and their variants have metamorphosed into objects of attack and cyber warfare. These issues have directed research focus to modeling infrastructural settings and infection scenarios, analyzing propagation mechanisms, and conducting studies that highlight optimized remedial measures.
Chukwunonso Henry Nwokoye
wiley   +1 more source

A study of chaos for processes under small perturbations II: rigorous proof of chaos [PDF]

Opuscula Mathematica, 2010
In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation \[\dot{z}=\left(1 + e^{i\kappa t} |z|^2\right)\bar{z}^2 - N e^{-i\frac{\pi}{3}}.\] Heteroclinic and homoclinic connections between two periodic solutions ...
Piotr Oprocha, Paweł Wilczyński
doaj   +1 more source

Generalized homoclinic solutions for the Swift–Hohenberg equation

Journal of Mathematical Analysis and Applications, 2012
The authors study the Swift-Hohenberg equation, which depends on one parameter and describes the onset of the Rayleigh-Bénard heat convection. By giving an explicit construction, they prove the existence of a homoclinic solution connecting a periodic orbit for every positive parameter.
Deng, Shengfu, Li, Xiaopei
openaire   +1 more source

The inner equation for generalized standard maps

, 2012
We study particular solutions of the inner equation associated to the splitting of separatrices on generalized standard maps. An exponentially small complete expression for their difference is obtained.
Baldomà, Imma, Martín, Pau
core   +1 more source

The Effects of Fluctuating Carrying Capacity on the Dynamics of a Holling‐Type III Predator–Prey Model

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the complex dynamics of a predator–prey system governed by the classical Lotka–Volterra model incorporating a Holling‐type III. To capture environmental variability, the prey’s carrying capacity is modeled as a periodic function, introducing a time‐dependent forcing into the system.
Ali Sarrah, Faizah J. Alanazi, Mehmet Yavuz, Sayed Saber, Mengxin Chen   +4 more
wiley   +1 more source