Results 1 to 10 of about 157,319 (379)

Dbar-approach to coupled nonlocal NLS equation and general nonlocal Reduction [PDF]

arXiv, 2021
The coupled nonlocal NLS equation is studied by virtue of the $2\times2$ Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The relations between the coupled nonlocal NLS potential and the solution of the Dbar-problem are constructed.
Xueru Wang, Junyi Zhu
arxiv   +3 more sources

Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions [PDF]

JMP 59, 051501 (2018), 2017
We study standard and nonlocal nonlinear Schr\"{o}dinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions respectively. By using the Hirota bilinear method we first find soliton solutions of the coupled NLS system of equations then using the ...
Gürses, Metin, Pekcan, Aslı
arxiv   +4 more sources

On the modulation instability development in optical fiber systems [PDF]

, 2010
Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation.
A. I. Dyachenko, A. I. Dyachenko, A. Picozzi, A. Picozzi, B. Kibler, C. Kharif, D. R. Solli, D. S. Agafontsev, E. B. Treacy, G. Chang, G. P. Agrawal, I. Cristiani, J. M. Dudley, J. M. Dudley, J. M. Dudley, K. Dysthe, N. Akhmediev, R. Jordan, V. E. Zakharov, V. P. Ruban, V. Zakharov   +20 more
arxiv   +3 more sources

On symmetry of traveling solitary waves for dispersion generalized NLS [PDF]

Nonlinearity, 2019
We consider dispersion generalized nonlinear Schr\"odinger equations (NLS) of the form $i \partial_t u = P(D) u - |u|^{2 \sigma} u$, where $P(D)$ denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results for traveling solitary waves in the case of powers $\sigma \in \mathbb{N}$.
Lars Bugiera, E. Lenzmann, A. Schikorra, J'er'emy Sok   +3 more
arxiv   +3 more sources

Integrable Hierarchies and Information Measures [PDF]

arXiv, 2007
In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimesional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrodinger (NLS) equation.
Ablowitz M, deBroglie L, Fisher R A, Jaynes E T, Kullback S, Lavrentiev A M, Madelung E, Ng W K Parwani R, Novikov S, Oktay K Pashaev, Parwani R J, Pashaev O K, Rajesh R Parwani, Salesi G Recami E   +13 more
arxiv   +3 more sources

Blowup for fractional NLS [PDF]

Journal of Functional Analysis, 2015
25 pages. Revised version, where some typos have been fixed.
Thomas Boulenger, D. Himmelsbach, E. Lenzmann   +2 more
semanticscholar   +6 more sources

Integrable inhomogeneous NLS equations are equivalent to the standard NLS [PDF]

Phys. Rev E 79, 015601(R) (2009), 2008
A class of inhomogeneous nonlinear Schr\"odinger equations (NLS), claiming to be novel integrable systems with rich properties continues appearing in PhysRev and PRL. All such equations are shown to be not new but equivalent to the standard NLS, which trivially explains their integrability features.
arxiv   +3 more sources

Blowup for Biharmonic NLS

Annales scientifiques de l'École normale supérieure, 2015
We consider the Cauchy problem for the biharmonic (i.\,e.~fourth-order) NLS with focusing nonlinearity given by $i \partial_t u = \Delta^2 u - \mu \Delta u -|u|^{2 \sigma} u$ for $(t,x) \in [0,T) \times \mathbb{R}^d$, where $0 4/d$, we prove a general ...
Thomas Boulenger, E. Lenzmann
semanticscholar   +6 more sources

Nanolipsome Modified with Inulin and Pea Protein Isolate Improve the Thermal Stability and Slow the Release of Anthocyanin at Simulated In Vitro Digestion and Hot Cocoa Beverage [PDF]

Foods
Anthocyanin (ACN) is a natural pigment with various biological activities, but their stability is compromised by external environmental factors, which limits their practical application in food processing.
Aniya, Lianlian Zhang, Yan Li, Xiaoji Fu
doaj   +2 more sources

NLS ground states on graphs [PDF]

Calculus of Variations and Partial Differential Equations, 2014
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the assumption is not ...
R. Adami, E. Serra, P. Tilli
semanticscholar   +5 more sources