Results 111 to 120 of about 32,605 (214)

Bound states of nonlinear Schrödinger equations with potentials tending to zero at infinity [PDF]

, 2009
In this paper, we are concerned with the existence of solutions to the N-dimensional nonlinear Schrödinger equation −ε2Δu+V(x)u=K(x)up with u(x)>0, u∈H1(RN), N⩾3 and ...
Zhang, Pingzheng, Yin, Huicheng, Huicheng Yin, Pingzheng Zhang   +3 more
core   +1 more source

Rational Solutions to the Fourth Equation of the Nonlinear Schrödinger Hierarchy

AppliedMath
This study concerns the research of rational solutions to the hierarchy of the nonlinear Schrödinger equation. In particular, we are interested in the equation of order 4. Rational solutions to the fourth equation of the NLS hierarchy are constructed and
Pierre Gaillard
doaj   +1 more source

On a class of nonlocal nonlinear Schrödinger equations and wave collapse [PDF]

, 2007
A similar type of nonlocal nonlinear Schrödinger (NLS) system arises in both water waves and nonlinear optics. The nonlocality is due to a coupling between the first harmonic and a mean term.
M. Ablowitz, I. Bakirtas, B. Ilan
core   +1 more source

Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations [PDF]

, 2015
A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates.
Pelinovsky, Dmitry, Yang, Jianke, Desyatnikov, Anton S   +2 more
core   +1 more source

Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

Alexandria Engineering Journal
In this study, the modified Sardar sub-equation (MSSE) method is capitalized to secure soliton solutions to the (1+1)-dimensional chiral nonlinear Schrödinger (NLS) equation.
Badr Saad T. Alkahtani
doaj   +1 more source

Spatial-temporal complexity in nonlinear Schrödinger equations [PDF]

, 1999
I study spatio-temporal complicated behaviors in the nonlinear Schrödinger (NLS) equation and its near-integrable generalized form, the perturbed NLS equation, under the periodic boundary condition.
Tan, Yu
core  

A $\overline{\partial }$-Dressing Method for the Kundu-Nonlinear Schrödinger Equation

Mathematics
In this paper, we employed the ∂¯-dressing method to investigate the Kundu-nonlinear Schrödinger equation based on the local 2 × 2 matrix ∂¯ problem. The Lax spectrum problem is used to derive a singular spectral problem of time and space associated with
Jiawei Hu, Ning Zhang
doaj   +1 more source

Non-Conservative Variational Approximation for Nonlinear Schrödinger Equations. [PDF]

, 2015
Recently, Galley [Phys. Rev. Lett. 110, 174301 (2013)] proposed an initial value problem formulation of Hamilton’s principle applied to non-conservative systems.
Rossi, J., Carretero-González, R., Kevrekidis, P. G.   +2 more
core  

Norm-inflation for periodic NLS equations in negative Sobolev spaces [PDF]

, 2015
18 pagesIn this paper we consider Schrödinger equations with nonlinearities of odd order 2σ + 1 on T^d. We prove that for σd≥2, they are strongly illposed in the Sobolev space H^s for any s < 0, exhibiting norm-inflation with infinite loss of regularity.
Carles, Rémi, Kappeler, Thomas
core   +1 more source

Water waves, nonlinear Schrödinger equations and their solutions

The Journal of the Australian Mathematical Society Series B Applied Mathematics, 1983
D. Peregrine
semanticscholar   +1 more source