Results 41 to 50 of about 902,254 (275)

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

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations [PDF]

, 2001
We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N ...
A. Ankiewicz, A. C. Scott, A. Hasegawa, C. Anastassiou, C. Yeh, D. N. Christodoulides, D. N. Christodoulides, G. P. Agrawal, J. U. Kang, K. Nakkeeran, M. H. Jakubowski, M. Lakshmanan, M. Mitchell, M. Mitchell, N. Akhmediev, N. Akhmediev, R. Hirota, R. Radhakrishnan, S. Chakravarty, S. V. Manakov, S. V. Manakov, T. Kanna, V. G. Makhan'kov, V. Kutuzov, W. Krolikowski   +24 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

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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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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Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions [PDF]

Proceedings of the Royal Society A, 2020
In this paper, we obtain the Nth-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique.
Tao Xu, Lingling Li, Min Li, Chunxia Li, Xuefeng Zhang   +4 more
semanticscholar   +1 more source

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
core   +1 more source

Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies [PDF]

, 2006
We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh.
A. Dimakis, A. Dimakis, B. Kupershmidt, B.F. Samsonov, B.G. Konopelchenko, C.-S. Chu, I.M. Gelfand ., J.A. Harvey, J.E. Moyal, J.J.C. Nimmo, K. Toda, K. Ueno, L. Tamassia, L.A. Dickey, L.D. Paniak, M. Błaszak, M. Hamanaka, M. Hamanaka, M. Hamanaka, M. Sakakibara, M. Sakakibara, Masashi Hamanaka, N. Marcus, O. Babelon, O. Lechtenfeld, O. Lechtenfeld, O. Lechtenfeld, P. Etingof, P. Etingof, R. S. Ward, R.J. Szabo, V.M. Goncharenko   +31 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