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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, 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, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +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

Existence and Spectral Stability Analysis of Viscous‐Dispersive Shock Profiles for Isentropic Compressible Fluids of Korteweg Type

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, Corrado Lattanzio, Ramón G. Plaza   +2 more
wiley   +1 more source

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems [PDF]

, 2005
We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations.
Yagasaki, Kazuyuki, Wagenknecht, T
core  

Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique

Open Physics
The present study investigates different types of wave symmetries in the (3+1)\left(3+1)-dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons,
Ceesay Baboucarr, Baber Muhammad Z., Ahmed Nauman, Shahid Naveed, Macías Siegfried, Macías-Díaz Jorge E.   +5 more
doaj   +1 more source

Existence and Stability for Traveling Waves of Fourth‐Order Semilinear Wave and Schrödinger Equations

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, Ross Parker, Atanas G. Stefanov   +2 more
wiley   +1 more source

Soliton-like solutions for a nonlinear doubly dispersive equation in an elastic Murnaghan's rod via Hirota's bilinear method

Open Physics
The purpose of this work is to study the physical phenomena of the doubly dispersive model that controls chaotic wave movement in the elastic Murnaghan’s rod.
Ceesay Baboucarr, Macías Siegfried, Baber Muhammad Z., Ahmed Nauman, Román-Loera Alejandro, Macías-Díaz Jorge E.   +5 more
doaj   +1 more source

Multiple front and pulse solutions in spatially periodic systems

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
wiley   +1 more source

Discrete embedded solitons [PDF]

, 2005
We address the existence and properties of discrete embedded solitons (ESs), that is localised waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both Chi(2)
Yagasaki, Y, Champneys, AR, Yagasaki, Kazuyuki, Malomed, BA   +3 more
core  

Solitonic wave solutions of a Hamiltonian nonlinear atom chain model through the Hirota bilinear transformation method

Open Physics
This study employs the Hirota bilinear transformation method to investigate solitary and soliton solutions resulting from different symmetry wave functions associated with nonlinear atom chain models. These models are complex dynamic systems that have an
Ceesay Baboucarr, Baber Muhammad Z., Ahmed Nauman, Macías Siegfried, Macías-Díaz Jorge E., Medina-Guevara María G.   +5 more
doaj   +1 more source