Results 61 to 70 of about 8,918 (208)
On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop
Tellus: Series A, Dynamic Meteorology and Oceanography, 2018 In this study, we discuss the role of the linear heating term and nonlinear terms associated with a non-linear feedback loop in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM), where (X, Y, Z) represent the ...
B.-W. Shen
doaj +1 more source
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
The Swift-Hohenberg equation with a nonlocal nonlinearity [PDF]
, 2013 It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional
Dawes, Jonathan H. P., Morgan, David
core +3 more sources
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most ...
Raffaele Folino +2 more
wiley +1 more source
Cross soliton and breather soliton for the (3+1) $(3+1)$-dimensional Yu–Toda–Sasa–Fukuyama equation
Advances in Difference Equations, 2019 Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach with perturbation parameter u0 $u_{0}$ and complexity of parameters, respectively.
Zhiqiang Pu, Zhigang Pan
doaj +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
Separatrix splitting at a Hamiltonian $0^2 i\omega$ bifurcation [PDF]
, 2014 We discuss the splitting of a separatrix in a generic unfolding of a degenerate equilibrium in a Hamiltonian system with two degrees of freedom. We assume that the unperturbed fixed point has two purely imaginary eigenvalues and a double zero one.
A Giorgilli +32 more
core +1 more source
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer +2 more
wiley +1 more source