Results 71 to 80 of about 48,721 (216)

M\"obius Symmetry of Discrete Time Soliton Equations

, 2002
We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various $q$-difference soliton ...
Hietarinta J., Hirota R., Hirota R., Hirota R., Jimbo M., Kupershmidt B., Narita Y., Ohta Y., Saito S., Tokihiro T.   +9 more
core   +1 more source

Soliton dynamics for fractional Schrödinger equations [PDF]

Applicable Analysis, 2013
22 ...
Secchi, S., Squassina, Marco
openaire   +3 more sources

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces

, 2007
Universal bi-Hamiltonian hierarchies of group-invariant (multicomponent) soliton equations are derived from non-stretching geometric curve flows $\map(t,x)$ in Riemannian symmetric spaces $M=G/H$, including compact semisimple Lie groups $M=K$ for $G=K ...
Anco, Anco, Anco, Anco, Anco, Athorne, Athorne, Bishop, Chou, Chou, Chou, Chou, Doliwa, Dorfman, Goldstein, Guggenheimer, Gurses, Helgason, Kobayashi, Lamb, Langer, Magri, Magri, Mari Beffa, Mari Beffa, Nakayama, Olver, Sanders, Sanders, Sergyeyev, Sharpe, Sokolov, Stephen C. Anco, Wang   +33 more
core   +4 more sources

Enhanced Nonlinear Optical Absorption Properties and Carrier Dynamics of Violet Phosphorene by Oxidation for Ultrafast Photonic Applications

ENERGY &ENVIRONMENTAL MATERIALS, EarlyView.
This study investigates the effects of oxidation treatment on the nonlinear optical absorption properties and carrier dynamics of two‐dimensional violet phosphorene (VP), elucidating the underlying physical mechanisms. Furthermore, ultrashort laser pulses are achieved utilizing the enhanced saturation absorption and shortened carrier relaxation ...
Bo Li, Han Pan, Qingling Tang, Zhongben Pan, Hongwei Chu, Ying Li, Dechun Li   +6 more
wiley   +1 more source

Direct Numerical Simulation of Magnetohydrodynamic Slip‐Flow Past a Stretching Surface Using Physics‐Informed Neural Network

Heat Transfer, EarlyView.
ABSTRACT Traditional numerical methods, such as finite difference methods (FDM), finite element methods (FEM), and spectral methods, often face meshing challenges and high computational cost for solving nonlinear coupled differential equations. Machine learning techniques, specifically Physics‐informed machine learning, address these obstacles by ...
Ahmad, Feroz Soomro, Husna Zafar
wiley   +1 more source

Soliton Fay identities. I. Dark soliton case

, 2014
We derive a set of bilinear identities for the determinants of the matrices that have been used to construct the dark soliton solutions for various models.
Vekslerchik, V. E.
core   +1 more source

Pulse Generation by On‐Chip Dispersion Compensation at 8 µm Wavelength

Laser &Photonics Reviews, EarlyView.
This work demonstrates on‐chip pulse generation at 8 μm$\mathrm{\mu}\mathrm{m}$ using chirped Bragg gratings in SiGe graded‐index photonic circuits to compensate the quadratic phase of quantum cascade laser frequency combs. With this approach pulses as short as 1.39 ps were produced, close to the transform limit, representing a key step toward compact,
Annabelle Bricout, Mathieu Bertrand, Philipp Täschler, Barbara Schneider, Victor Turpaud, Stefano Calcaterra, Davide Impelluso, Marco Faverzani, David Bouville, Jean‐René Coudevylle, Samson Edmond, Etienne Herth, Carlos Alonso‐Ramos, Laurent Vivien, Jacopo Frigerio, Giovanni Isella, Jérôme Faist, Delphine Marris‐Morini   +17 more
wiley   +1 more source

Unification of integrable q-difference equations

Electronic Journal of Differential Equations, 2015
This article presents a unifying framework for q-discrete equations. We introduce a generalized q-difference equation in Hirota bilinear form and develop the associated three-q-soliton solutions which are described in polynomials of power functions ...
Burcu Silindir, Duygu Soyoglu
doaj  

Integrable Theory of the Perturbation Equations

, 1996
An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries, linear ...
B. Fuchssteiner, Ballantyne, Chen, Currò, David, Dorfman, Elgin, Fuchssteiner, Fuchssteiner, Fuchssteiner, Fuchssteiner, Gel'fand, Grimshaw, Herman, Karpman, Keener, Kivshar, Kodama, Kraenkel, Kraenkel, Ma, Ma, Ma, Ma, Ma, Ma, Magri, Matsuno, Oevel, Olver, Schwarz, Tamizhmani, Tanaka, W.X. Ma, Wadati, Zakharov   +35 more
core   +2 more sources