Results 41 to 50 of about 9,595 (205)

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

Variational Approach to Impulsive Problems: A Survey of Recent Results

Abstract and Applied Analysis, 2014
We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.
Fang-fang Liao, Juntao Sun
doaj   +1 more source

Multibump solutions of a class of second-order discrete Hamiltonian systems [PDF]

, 2013
For a class of second-order discrete Hamiltonian systems $\Delta^2x(t-1)-L(t)x(t)+V'_x(t,x(t))=0$, we investigate the existence of homoclinic orbits by applying variational method, where $L$ and $V(\cdot,x)$ are periodic functions.
Zhang, Xu
core  

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

Multiplicity results for the Neumann boundary value problem

Mathematical Modelling and Analysis, 2007
We provide multiplicity results for the Neumann boundary value problem, when the second order differential equation is of the form x” = f(x).
Svetlana Atslega
doaj   +1 more source

Are physiological oscillations physiological?

The Journal of Physiology, Volume 604, Issue 9, Page 3672-3693, 1 May 2026.
Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
wiley   +1 more source

Homoclinic solutions for Hamiltonian system with impulsive effects

Advances in Difference Equations, 2018
In this article, we investigate a class of impulsive Hamiltonian systems with a p-Laplacian operator. By establishing a series of new sufficient conditions, the existence of homoclinic solutions to such type of systems is revealed.
Jian Liu, Lizhao Yan, Fei Xu, Mingyong Lai   +3 more
doaj   +1 more source

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

Full-time dynamics of modulational instability in spinor Bose-Einstein condensates

, 2007
We describe the full-time dynamics of modulational instability in F=1 spinor Bose-Einstein condensates for the case of the integrable three-component model associated with the matrix nonlinear Schroedinger equation. We obtain an exact homoclinic solution
A. R. Its, E. V. Doktorov, Evgeny V. Doktorov, M. J. Ablowitz, N. N. Akhmediev, N. N. Akhmediev, O. C. Wright, O. C. Wright, S. P. Novikov, S. Trillo, Vassilis M. Rothos, Y. Li, Yuri S. Kivshar   +12 more
core   +1 more source