Results 61 to 70 of about 274 (149)

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

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

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

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

On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations

Mathematics
This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients.
José M. Escorcia, Erwin Suazo
doaj   +1 more source

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Journal of Advanced Research, 2019
In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity ...
Weitian Yu, Qin Zhou, Mohammad Mirzazadeh, Wenjun Liu, Anjan Biswas   +4 more
doaj   +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

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

Scattering and Blow‐Up Dichotomy of the Energy‐Critical Nonlinear Schrödinger Equation With the Inverse‐Square Potential

Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 9225-9240, 30 May 2025.
ABSTRACT In this paper, we consider the energy critical nonlinear Schrödinger equation with a repulsive inverse square potential. In particular, we deal with radial initial data, whose energy is equal to the energy of static solution to the corresponding nonlinear Schrödinger equation without a potential.
Masaru Hamano, Masahiro Ikeda
wiley   +1 more source

Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

Results in Physics, 2019
We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear
Hamdy I. Abdel-Gawad, A. Biswas, A.S. Alshomrani, M. Belic   +3 more
doaj   +1 more source