Results 41 to 50 of about 274 (149)

Numerical Study of Transverse (In‐)Stability of Solitary Waves in the Cubic–Quintic Nonlinear Schrödinger Equation

Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.
ABSTRACT We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain Rx×TLy$\mathbb {R}_x \times \mathbb {T}_{L_y}$. This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated.
Christian Klein, Christof Sparber
wiley   +1 more source

Integrable discretisations and Yang–Baxter maps for super nonlinear Schrödinger systems

Nuclear Physics B
We construct an integrable Grassmann-extended vertex-bond discrete system, which can be restricted to the Grassmann-extended Adler–Yamilov system of partial difference equations, and we derive a Darboux matrix and a Bäcklund transformation for the latter.
Sotiris Konstantinou-Rizos
doaj   +1 more source

Solution of the Davey–Stewardson equation using homotopuy analysis method

Nonlinear Analysis, 2010
In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been
H. Jafari, M. Alipour
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

Dispersion‐Less Dissipative Soliton Fiber Laser

Laser &Photonics Reviews, Volume 20, Issue 6, 18 March 2026.
A dispersion‐less fiber laser architecture generates high‐energy, pedestal‐free picosecond pulses without resorting to conventional pulse stretching. This energy‐managed laser achieves remarkable flexibility in pulse parameters, delivering up to 0.54 μJ$\mathrm{\mu}\mathrm{J}$ pulses with minimal spectral distortion using standard telecom components ...
Mostafa I. Mohamed, Aurélien Coillet, Philippe Grelu   +2 more
wiley   +1 more source

Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

Symmetry, Integrability and Geometry: Methods and Applications, 2006
Addition of higher nonlinear terms to the well known integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel Eckhaus-Kundu hierarchy,
Anjan Kundu
doaj  

Dispersive Wave Focusing in Shoaling Water With Currents

Journal of Geophysical Research: Oceans, Volume 131, Issue 3, March 2026.
Abstract A methodology creating dispersive focusing waves on constant depth, originally proposed by Rapp and Melville (1990), https://doi.org/10.1098/rsta.1990.0098, has provided a wide range of applications studying nonlinear waves, wave breaking, and rogue waves in the open ocean.
Y. Watanabe, T. Davey, D. M. Ingram
wiley   +1 more source

Soliton cluster solutions of nonlinear Schrödinger equations with variable coefficients in Bessel lattice

Results in Physics
The goal of this article is to obtain soliton cluster solutions of (2 + 1)-dimensional nonlinear variable coefficient Schrödinger equations through computerized symbolic computation.
Shaofu Wang
doaj   +1 more source

Numerical Study of a Nonlocal Nonlinear Schrödinger Equation (MMT Model)

Studies in Applied Mathematics, Volume 156, Issue 3, March 2026.
ABSTRACT In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long‐term behavior of solutions, and we identify the conditions under which the solutions of the Cauchy problem associated with this equation are bounded globally in time in the ...
Amin Esfahani, Gulcin M. Muslu
wiley   +1 more source

Analytical soliton solutions of the perturbed fractional nonlinear Schrödinger equation with space–time beta derivative by some techniques

Results in Physics, 2023
Nonlinear fractional-order evolution equations are fundamental strategies for simulating nonlinear phenomena on a large scale in technology, science, and engineering.
M. Ali Akbar, Farah Aini Abdullah, Md. Morshedul Haque   +2 more
doaj   +1 more source