Results 31 to 40 of about 40,499 (216)

Novel soliton solutions to a (2+1)-dimensional breaking soliton equation

Partial Differential Equations in Applied Mathematics, 2022
In this paper, a Hirota bilinear form is presented for a (2+1)-dimensional breaking soliton equation. Novel N-soliton solutions are constructed through an application of the Hiorta direct method.
Qi Chen, Xiao-ming Zhu, Jian-bing Zhang
doaj   +1 more source

N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation

Advances in Mathematical Physics, 2014
The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK) equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained.
Jian Zhou, Xiang-Gui Li, Deng-Shan Wang
doaj   +1 more source

The Integrability of a New Fractional Soliton Hierarchy and Its Application

Advances in Mathematical Physics, 2022
Two fractional soliton equations are presented generated from the same spectral problem involved in a fractional potential by the zero-curvature representations. They are a kind of special reductions of the famous AKNS system.
Xiao-ming Zhu, Jian-bing Zhang
doaj   +1 more source

Young diagrams and N-soliton solutions of the KP equation

, 2004
We consider $N$-soliton solutions of the KP equation, (-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An $N$-soliton solution is a solution $u(x,y,t)$ which has the same set of $N$ line soliton solutions in both asymptotics $y\to\infty$ and $y\to -\infty$.
Biondini G, Gantmacher F R, Griffiths P, Hirota R, Infeld E, Kadomtsev B B, Pashaev O K Yerbag-Francisco M L, Sato M, Yuji Kodama   +8 more
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N$N$‐Soliton Matrix mKdV Solutions: Some Special Solutions Revisited

Studies in Applied Mathematics
ABSTRACTIn this article, a general solution formula is derived for the ‐matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as ‐solitons (in the sense of Goncharenko) with common phase matrix.
Carillo S., Lo Schiavo M., Schiebold C.
openaire   +3 more sources

Nonlocal Coupled HI-MKdV Systems

, 2019
We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the help of ...
Pekcan, Aslı
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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
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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
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Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters [PDF]

, 2009
We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation).
Demoulin A., Demoulin A., Demoulin A., J. J. C. Nimmo, Kaptsov O. V., Mikhailov A. V., S. N. M. Ruijsenaars, Tzitzeica G., Tzitzeica G., Zhiber A. V.   +9 more
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Nonlinear superposition between lump soliton and other nonlinear localized waves for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Results in Physics, 2023
In the previous studies, the authors have reported the lump soliton collided with other nonlinear localized waves for (2+1)-dimensional Korteweg–de Vries–Sawada-Kotera–Ramani equation.
Longxing Li, Zhengde Dai, Bitao Cheng, Rubing Li   +3 more
doaj   +1 more source