Results 21 to 30 of about 5,863,832 (163)
Mathematics, 2023 A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method.
Jian Zhang +3 more
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Advances in Difference Equations, 2018 Discrete N-fold Darboux transformation (DT) is used to derive new bright and dark multi-soliton solutions of two higher-order Toda lattice equations. Propagation and elastic interaction structures of such soliton solutions are shown graphically.
Nan Liu, Xiao-Yong Wen, Ling Xu
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Journal of Ocean Engineering and Science, 2023 In the fields of oceanography, hydrodynamics, and marine engineering, many mathematicians and physicists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenomena, one of which is a (3+1)-dimensional Burgers ...
Sachin Kumar, Amit Kumar, Brij Mohan
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Partial Differential Equations in Applied Mathematics, 2022 In this paper, two modified KdV (MKdV) equations, one is real and the other is complex, are investigated. By applying the Hirota bilinear operator theory and computer algebra, the corresponding bilinear forms of these two MKdV equations are successfully ...
Yong-Li Sun, Jian-Ping Yu
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Various exact wave solutions for KdV equation with time-variable coefficients
Journal of Ocean Engineering and Science, 2022 In this study, we investigate the (2 + 1)-dimensional Korteweg-De Vries (KdV) equation with the extension of time-dependent coefficients. A symbolic computational method, the simplified Hirota’s method, and a long-wave method are utilized to create ...
Hajar F. Ismael +2 more
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Results in Physics, 2021 In this paper, the generalized shallow water equation (GSWE) is carefully investigated via three state-of-the-art integration schemes, namely the simplified linear superposition principle, velocity resonance, and the trial function method, respectively ...
Chun-Ku Kuo, Behzad Ghanbari
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Two-peak soliton in the CKP hierarchy [PDF]
, 2006 We present a systematic approach to the construction of soliton solutions for the 5-reduction of the C-type sub-hierarchy for the Kadomtsev–Petviashvili (CKP) hierarchies starting from the general τ-function τ(n+k) of the Kadomtsev–Petviashvili (KP ...
Cheng, Yi +2 more
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On soliton solutions of the Wu-Zhang system
Open Physics, 2016 In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ) system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.
Inc Mustafa +5 more
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Dynamical structure of truncated M−fractional Klein–Gordon model via two integral schemes
Results in Physics, 2023 In this work, the Truncated M−fractional Klein–Gordon (tM-fKG) equation is integrated by implementing the exp(-ϕ(ξ))-expansion and new form of modified Kudryashov’s schemes.
Harun-Or-Roshid +5 more
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Solving bi-directional soliton equations in the KP hierarchy by gauge transformation [PDF]
, 2006 We present a systematic way to construct solutions of the (n = 5)-reduction of the BKP and CKP hierarchies from the general τ function τn+k of the KP hierarchy.
Cheng, Yi +4 more
core +1 more source