Results 51 to 60 of about 3,396,163 (214)
Sharp Upper Bound for Amplitudes of Finite‐Gap Solutions of the Modified Korteweg‐de Vries Equation
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT A sharp upper bound is established for the amplitudes of finite‐gap solutions of the focusing modified Korteweg–de Vries equation. The proof shows that the optimization can be carried out entirely within the finite‐dimensional hierarchy, without explicit integration of the finite‐gap solution. The maximal amplitude is expressed in terms of the
Otis C. Wright III
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
Global bifurcation of homoclinic solutions of Hamiltonian systems
Discrete and Continuous Dynamical Systems, 2003 We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
openaire +4 more sources
Topics in Cognitive Science, Volume 18, Issue 3, July 2026.Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
wiley +1 more source
Linearly independent homoclinic bifurcations parameterized by a small function [PDF]
, 2007 In this paper we discuss a small nonautonomous perturbation of an autonomous system on Rn which has a homoclinic solution. Regarding the small perturbation as a parameter in an appropriate space of functions we discuss various situations of co-existence ...
Zhang, Weinian +3 more
core +1 more source
Homoclinic orbits in Kerr-Newman black holes
, 2023 We present the exact solutions of the homoclinic orbits for the timelike geodesics of the particle on the general nonequatorial orbits in the Kerr-Newman black holes. The homoclinic orbit is the separatrix between bound and plunging geodesics, a solution
Lin, Chi-Yong +7 more
core +1 more source
Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations
Boundary Value Problems, 2009 This paper investigates the singular differential equation (p(t)u′)′=p(t)f(u), having a singularity at t=0. The existence of a strictly increasing solution (a homoclinic solution) satisfying u′(0)=0, u(∞)=L>0 is proved ...
Irena Rachůnková +1 more
doaj +1 more source
Periodic and Homoclinic Solutions of Extended Fisher–Kolmogorov Equations
Journal of Mathematical Analysis and Applications, 2000 The authors study the existence of periodic and homoclinic solutions to fourth-order semilinear equations via variational methods.
Tersian, Stepan, Chaparova, Julia
openaire +2 more sources
Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.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 +4 more
wiley +1 more source