Results 41 to 50 of about 40,499 (216)

Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy

, 1997
The algebraic matrix hierarchy approach based on affine Lie $sl (n)$ algebras leads to a variety of 1+1 soliton equations. By varying the rank of the underlying $sl (n)$ algebra as well as its gradation in the affine setting, one encompasses the set of ...
A H Zimerman, Aratyn H, Burroughs N J, Cheng Y, de Groot M F, Dickey L A, Drinfel'd V G, Drinfel'd V G, Fordy A P, Fordy A P, H Aratyn, J F Gomes, Kac V C, Kac V G, L A Ferreira, Oevel W, Wilson G, Wilson G   +17 more
core   +1 more source

On the N-Solitons Solutions in the Novikov-Veselov Equation [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2013
We construct the $N$-solitons solution in the Novikov-Veselov equation from the extended Moutard transformation and the Pfaffian structure. Also, the corresponding wave functions are obtained explicitly. As a result, the property characterizing the $N$-solitons wave function is proved using the Pfaffian expansion.
openaire   +4 more sources

Dynamics of resonant soliton, novel hybrid interaction, complex N-soliton and the abundant wave solutions to the (2+1)-dimensional Boussinesq equation

Alexandria Engineering Journal
The presented work concerns with some novel solutions of the (2+1)-dimensional Boussinesq equation (BE), which acts as an important model for shallow water wave.
Kang-Jia Wang, Feng Shi, Shuai Li, Peng Xu   +3 more
doaj   +1 more source

The N-soliton solutions to the M-components nonlinear Schrödinger equations by the Riemann–Hilbert approach

Partial Differential Equations in Applied Mathematics, 2022
In this paper, the main work is to study the N-soliton solutions for the M-component nonlinear Schrödinger equations, the matrix Riemann–Hilbert problem is constructed for this integrable hierarchies by analyzing the block matrix spectral problem of the ...
Jian Li, Tiecheng Xia
doaj   +1 more source

New dynamical behaviors for a new extension of the Shallow water model

Results in Physics, 2022
The aim of this work, is to construct some novel solutions for a new extension of the shallow water model in (3+1)-dimensions. Based on two methods namely; simplified Hirota’s method and a long-wave method a class of solutions are reported.
Jian-Guo Liu, Hajar F. Ismael, Hasan Bulut   +2 more
doaj   +1 more source

Vertex operator for the non-autonomous ultradiscrete KP equation

, 2009
We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.Comment: 9 ...
Nagai H, Nakata Y, Shinzawa N, Tokihiro T, Yoichi Nakata   +4 more
core   +1 more source

Study of Free‐Space Optical Quantum Network: Review and Prospectives

Advanced Science, EarlyView.
Free from the constraints of fiber connections, free‐space quantum network enables longer and more flexible quantum network connections. This review summarizes and comparatively analyzes free‐space quantum network experiments based on ground stations, satellites, and mobile platforms.
Hua‐Ying Liu, Zhenda Xie, Shining Zhu
wiley   +1 more source

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation

Scientific Reports, 2023
In this paper, the exact solutions of generalized nonlinear Schrödinger (GNLS) equation are obtained by using Darboux transformation(DT). We derive some expressions of the 1-solitons, 2-solitons and n-soliton solutions of the GNLS equation via ...
Chengcheng Fan, Li Li, Fajun Yu
doaj   +1 more source

N-soliton solutions to the DKP equation and Weyl group actions

, 2006
We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, \[ {\begin{array}{llll} (-4D_xD_t+D_x^4+3D_y^2) \tau_n\cdot\tau_n=24\tau_{n-1}\tau_{n+1}, (2D_t+D_x^3\mp 3D_xD_y) \tau_{n\pm 1}\cdot\tau_n=0 \end{array} \quad n ...
Biondini G, Ishikawa M, Isojima S, Jimbo M, Kac V G, Ken-Ichi Maruno, Kodama Y, Yuji Kodama   +7 more
core   +2 more sources

Asymptotic $N$-soliton-like solutions of the fractional Korteweg–de Vries equation

Revista Matemática Iberoamericana, 2022
We construct N -soliton solutions for the fractional Korteweg–de Vries (fKdV) equation \partial_t u - \partial_x(|D|^{\alpha}u - u^2 )=0,
openaire   +5 more sources