Results 51 to 60 of about 8,918 (208)

Homoclinic Orbits In Slowly Varying Oscillators [PDF]

, 1987
We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
core   +1 more source

Global bifurcation of homoclinic solutions of Hamiltonian systems

Discrete & Continuous Dynamical Systems - A, 2003
We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
openaire   +4 more sources

Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

Abstract and Applied Analysis, 2014
We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS) where -∞
Ziheng Zhang, Fang-Fang Liao, Patricia J. Y. Wong   +2 more
doaj   +1 more source

Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
doaj   +1 more source

Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

, 2013
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations.
Choudhury, S. Roy, Gambino, G., Rehman, T.   +2 more
core   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Global bifurcation of homoclinic solutions

Journal of Differential Equations
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine contemporary functional analytical methods from the abstract bifurcation theory for Fredholm operators with tools ...
Iacopo P. Longo, Christian Pötzsche, Robert Skiba   +2 more
openaire   +2 more sources

Positive homoclinic solutions to some Schrödinger type equations

Differential and Integral Equations, 2016
By means of variational methods we prove the existence of a positive, homoclinic solution to an equation of the kind u''=au-bu^p, where p>1, and both coefficients a(x), b(x) are positive and asymptotically constant. Our main result requires a control from above on the ratios .between the supremum of a(x) and its limit at infinity and between the limit ...
GAVIOLI, Andrea, Sanchez, Luis
openaire   +3 more sources

Dissipative periodic and chaotic patterns to the KdV--Burgers and Gardner equations [PDF]

, 2019
We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems and Shil'nikov's analysis.
Adams, Ronald, Mancas, Stefan C.
core   +3 more sources

Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting

Journal of Applied Mathematics, 2014
Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the ...
Mingzhan Huang, Xinyu Song
doaj   +1 more source