Results 61 to 70 of about 52,211 (225)

Numerical Solitons of Generalized Korteweg-de Vries Equations

, 2005
We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We
Camassa, Fokas, Gardner, Houde Han, Rosenau, Rosenau, Zabusky, Zhenli Xu   +7 more
core   +2 more sources

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

, 2003
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons.
Ablowitz, Ablowitz, Beals, Beals, Beals, Fokas, Fokas, Fokas, Gagnon, Jianke Yang, Kaup, Leon, Manakov, Manakov, Manakov, Pelinovsky, Shabat, Shchesnovich, Shchesnovich, Tsuru, Valery S. Shchesnovich, Villarroel, Wadati, Yang, Zakharov, Zakharov, Zakharov, Zakharov, Zakharov, Zakharov, Zhou, Zhou   +31 more
core   +1 more source

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

Solitons in supersymmetric sigma-models with torsion

, 1995
We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in its supersymmetry algebra.The bound is saturated by ...
Abraham, Abraham, Alvarez-Gaumé, Atkinson, Bogomol'nyi, G. Papadopoulos, Gates, Gibbons, Hitchin, Howe, Howe, Hull, Hull, P.K. Townsend, Papadopoulos, Papadopoulos, Pedersen, Witten   +17 more
core   +1 more source

Constructing N-soliton solution for the mKdV equation through constrained flows [PDF]

, 2001
Based on the factorization of soliton equations into two commuting integrable x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via its x- and t-constrained flows.
Ablowitz M, Cao Cewen, Dubrovin B A, Eilbeck J C, Faddeev L D, Huihui Dai, Its A, Newell A C, Ragnisco O, Sklyanin E K, Sklyanin E K, Yunbo Zeng, Zeng Yunbo, Zeng Yunbo, Zeng Yunbo   +14 more
core   +2 more sources

Soliton solutions of relativistic Hartree equations [PDF]

Journal of Physics A: Mathematical and General, 1993
We study a model based on $N$ scalar complex fields coupled to a scalar real field, where all fields are treated classically as c-numbers. The model describes a composite particle made up of $N$ constituents with bare mass $m_0$ interacting both with each other and with themselves via the exchange of a particle of mass $μ_0$.
openaire   +3 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

Yang-Baxter and reflection maps from vector solitons with a boundary [PDF]

, 2014
Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on the half-line.
Ablowitz M, Ablowitz M J, Caudrelier V, Faddeev L, Gerdjikov V S, Manakov S V, Mintchev M, Q C Zhang, Sklyanin E, V Caudrelier, Veselov A P   +10 more
core   +2 more sources

Strain Imaging of GaAs by Stimulated Raman Scattering Microscopy

Journal of Raman Spectroscopy, EarlyView.
Telecom‐wavelength stimulated Raman scattering (SRS) microscopy is developed for high‐throughput, nondestructive characterization of gallium arsenide (GaAs). By overcoming optical absorption limits of conventional Raman systems, this technique enables precise visualization of LO phonon frequency variations (< 0.2‐cm−1$$ {}^{-1} $$ precision).
Yuki Sano, Yasuyuki Ozeki
wiley   +1 more source