Results 31 to 40 of about 3,238 (183)
Partial Differential Equations in Applied Mathematics, 2022 Bilinearization of nonlinear partial differential equations (PDEs) is essential in the Hirota method, which is a widely used and robust mathematical tool for finding soliton solutions of nonlinear PDEs in a variety of fields, including nonlinear dynamics, mathematical physics, and engineering sciences.
Sachin Kumar, Brij Mohan
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Mathematics, 2022 In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rational
Ruijuan Li +5 more
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Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies [PDF]
, 2017 In this paper, we give a procedure of how to discretize the recursion operators by considering unified bilinear forms of integrable hierarchies. As two illustrative examples, the unified bilinear forms of the AKNS hierarchy and the KdV hierarchy are ...
Hu, Xingbiao, Yu, Guofu, Zhang, Yingnan
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The symmetry breaking solutions of the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system
Results in Physics, 2023 The (2+1)-dimensional B-type Kadomtsev–Petviashvili equation is an integrable model, which can be used to describe the shallow water wave in a fluid. In this paper, the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system is induced via the principle ...
Peng Dong +3 more
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Novel physical nonlinear structures in Saturn’s magnetosphere: Ion-acoustic solitons, lumps, and horseshoe-like nonlinear waves [PDF]
AIP AdvancesIn this paper, new analytical physical solutions to the Kadomtsev–Petviashvili–Bergers’ (KPB) equation in the multicomponent plasmas of Saturn are reported.
Weaam Alhejaili +2 more
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Frontiers in Physics, 2020 In this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz.
Aliyu Isa Aliyu +6 more
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Algebraic solutions of the Hirota bilinear form for the Korteweg-de Vries and Boussinesq equations
Indian Journal of Pure and Applied Mathematics, 2015 In this paper, the authors analyze the Hirota bilinear forms for the Korteweg-de Vries (K-dV) equation and the Boussinesq equation from the point of view of symmetry analysis to reduce the \((1+1)\) evolution equations to ordinary differential equations.
Krishnakumar, K. +2 more
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Journal of Function Spaces, 2021 In this paper, we study the (3+1)-dimensional variable-coefficient nonlinear wave equation which is taken in soliton theory and generated by utilizing the Hirota bilinear technique.
Xuejun Zhou +5 more
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Partial Differential Equations in Applied Mathematics, 2021 New generalized (2+1)-dimensional Boussinesq system with variable coefficients has been introduced. A double Wronskian solutions has been formulated to the new system under certain constraints on the variable coefficients.
Alrazi Abdeljabbar
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New solution of the $\mathcal{N}=2$ Supersymmetric KdV equation via Hirota methods
, 2012 We consider the resolution of the $\mathcal{N}=2$ supersymmetric KdV equation with $a=-2$ ($SKdV_{a=-2}$) from the Hirota formalism. For the first time, a bilinear form of the $SKdV_{a=-2}$ equation is constructed. We construct multisoliton solutions and
Carstea A S +8 more
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