Results 51 to 60 of about 2,498 (146)

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Rogue waves and downshifting in the presence of damping [PDF]

Natural Hazards and Earth System Sciences, 2011
Recently Gramstad and Trulsen derived a new higher order nonlinear Schrödinger (HONLS) equation which is Hamiltonian (Gramstad and Trulsen, 2011). We investigate the effects of dissipation on the development of rogue waves and downshifting by adding an ...
A. Islas, C. M. Schober
doaj   +1 more source

On Standing Waves of 1D Nonlinear Schrödinger Equation With Triple Power Nonlinearity

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT For the one‐dimensional nonlinear Schrödinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of nonexistence and curves of stability change on the parameter planes.
Theo Morrison, Tai‐Peng Tsai
wiley   +1 more source

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Mathematics
The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity
Natanael Karjanto
doaj   +1 more source

Fractional isospectral and non-isospectral AKNS hierarchies and their analytic methods for N-fractal solutions with Mittag-Leffler functions

Advances in Difference Equations, 2021
Ablowitz–Kaup–Newell–Segur (AKNS) linear spectral problem gives birth to many important nonlinear mathematical physics equations including nonlocal ones.
Bo Xu, Yufeng Zhang, Sheng Zhang
doaj   +1 more source

Stochastic Multisymplectic PDEs and Their Structure‐Preserving Numerical Methods

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637].
Ruiao Hu, Linyu Peng
wiley   +1 more source

Existence and Orbital Stability of Standing‐Wave Solutions of the Nonlinear Logarithmic Schrödinger Equation On a Tadpole Graph

Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.
ABSTRACT This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS‐log) on a tadpole graph, namely, a graph consisting of a circle with a half‐line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing ...
Jaime Angulo Pava, Andrés Gerardo Pérez Yépez   +1 more
wiley   +1 more source

Rogue waves and periodic solutions of a nonlocal nonlinear Schrödinger model

Physical Review Research, 2020
In the present paper, a nonlocal nonlinear Schrödinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations by considering them as fixed points in space-time.
C. B. Ward, P. G. Kevrekidis, T. P. Horikis, D. J. Frantzeskakis   +3 more
doaj   +1 more source

Propagation of weakly nonlinear axial waves of nanorods embedded in a viscoelastic medium

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 6, June 2025.
Abstract Nonlinear equations play a fundamental role in explaining complex systems in science and technology, particularly in the field of wave propagation. Nonlocal elasticity theory is a general method for analyzing nanostructures at the nanoscale. The current work utilizes Eringen's nonlocal constitutive equations to solve the nonlinear equations of
Guler Gaygusuzoglu, Zehra Pinar Izgi, Aydin Ozmutlu   +2 more
wiley   +1 more source

Impact of fifth order dispersion on soliton solution for higher order NLS equation with variable coefficients

Journal of Ocean Engineering and Science, 2020
In this paper, the variable coefficient nonlinear Schrödinger equation with fifth order dispersion in the inhomogeneous optical fiber is investigated to study the impact of fifth order dispersion on attosecond soliton propagation.
Angelin Vithya, M.S. Mani Rajan
doaj   +1 more source