Results 101 to 110 of about 51,683 (232)

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

Solitonic solutions and gravitational solitons: an overview

, 2021
In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be interpreted as a soliton solution in the case of axial symmetry.
openaire   +1 more source

Novel multi-soliton solutions of the breaking soliton equation

Acta Physica Sinica, 2003
Hirota bilinear method is a very effective method for solving nonlinear evolution equations. In this paper, by further generalizing this method, we obtain novel multi-soliton solutions of (2+1)-dimensional breaking soliton equation.
null Zhang Jie-Fang, null Guo Guan-Ping
openaire   +1 more source

Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar, Khaled A. Gepreel, Reham M. A. Shohib, Yakup Yildirim   +3 more
wiley   +1 more source

On one-soliton solutions of the Q2 equation in the ABS list

Advances in Difference Equations, 2019
In this paper, we derive seed and 1-soliton solutions of the Q2 equation in the Adler–Bobenko–Suris list. The seed solutions of Q2 are obtained using those of Q1(δ) $\mbox{Q}1(\delta)$ and an non-auto Bäcklund transformation connecting them.
Qiang Cheng, Cheng Zhang, Danda Zhang, Da-jun Zhang   +3 more
doaj   +1 more source

Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems

, 2018
It is found that two different celebrate models, the Korteweg de-Vrise (KdV) equation and the Boussinesq equation, are linked to a same model equation but with different nonlocalities. The model equation is called the Alice-Bob KdV (ABKdV) equation which
Lou, S. Y.
core  

A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

, 2009
Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two ...
A.I. Bobenko, C.M. Viallet, F.W. Nijhoff, F.W. Nijhoff, Frank Nijhoff, H.D. Wahlquist, J. Atkinson, J. Atkinson, J. Hietarinta, J. Weiss, J. Weiss, James Atkinson, R. Hirota, R. Hirota, V.E. Adler, V.E. Adler, V.E. Adler, V.E. Adler, V.E. Zakharov, V.E. Zakharov, V.M. Buchstaber, Y. Ohta   +21 more
core   +1 more source

Interaction of Dirac δ$$ \delta $$‐Waves in the Inviscid Levine and Sleeman Chemotaxis Model

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This article investigates interactions of δ$$ \delta $$‐shock waves in the inviscid Levine and Sleeman chemotaxis model ut−λ(uv)x=0$$ {u}_t-\lambda {(uv)}_x=0 $$, vt−ux=0$$ {v}_t-{u}_x=0 $$. The analysis employs a distributional product and a solution concept that extends the classical solution concept.
Adelino Paiva
wiley   +1 more source

Mathematical analysis of shallow water wave and the generalized Hirota-Satsuma-Ito models: Soliton solutions and their interactions

Results in Applied Mathematics
This study investigates the mathematical properties and soliton dynamics of the (2+1)-dimensional extended Shallow Water Wave (eSWW) and the generalized Hirota-Satsuma-Ito (gHSI) models by Hirota bilinear scheme.
M. Belal Hossen, Md. Towhiduzzaman, Harun-Or-Roshid, K. M. Abdul A. Woadud   +3 more
doaj   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source