Soliton solutions by means of Hirota bilinear forms
Partial Differential Equations in Applied Mathematics, 2022 The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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An efficient algorithm of logarithmic transformation to Hirota bilinear form of KdV-type bilinear equation [PDF]
Applied Mathematics and Computation, 2011 14pages
Jingsong He
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Results in Physics, 2023 In this article, a new dynamical system equation is constructed, named the (3+1)-dimensional Hirota-bilinear-like equation. The new ‘like’ equation has more nonlinear terms than the original equation while they have the same bilinear form.
Wenting Li, Ailing Jiao
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Exact breather waves solutions in a spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions [PDF]
Scientific ReportsIn this article, the spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time.
Qunyan Zou +6 more
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Results in Physics, 2021 In this paper, Hirota’s bilinear form has been employed to find novel lump waves solutions for the generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation. This equation is one of the most widely used equations in the field of fluid mechanics. Using the employed technique in the paper, several different categories of solutions to the equation are ...
Behzad Ghanbari
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Lump, lump-periodic, lump-soliton and multi soliton solutions for the potential Kadomtsev-Petviashvili type coupled system with variable coefficients [PDF]
Scientific ReportsIn this article, the potential Kadomtsev-Petviashvili (pKP) type coupled system with variable coefficients is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time. In this framework, Hirota
Haiwei Chen +8 more
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An exploration of the (3+1)-dimensional negative order KdV-CBS model: Wave solutions, Bäcklund transformation, and complexiton dynamics. [PDF]
PLoS ONEThis research paper focuses on the study of the (3+1)-dimensional negative order KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation, an important nonlinear partial differential equation in oceanography.
Miguel Vivas-Cortez +4 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.
K M Tamizhmani +2 more
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Bilinear Identities and Hirota's Bilinear Forms for an Extended Kadomtsev-Petviashvili Hierarchy [PDF]
Journal of Nonlinear Mathematical Physics, 2021 In this paper, we construct the bilinear identities for the wave functions of an extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchy with particular extended flows (2008, Phys. Lett. A, 372: 3819). By introducing an auxiliary parameter (denoted by $z$), whose flow corresponds to the so-called squared eigenfunction symmetry of KP ...
Lin, Runliang, Liu, Xiaojun, Zeng, Yunbo
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Bilinear form and exact solutions for a new extended (2+1)-dimensional Boussinesq equation
Results in Physics, 2021 In this article, a new extended (2+1)-dimensional Boussinesq equation which can be used to describe the propagation of shallow water waves, was investigated.
Ping Cui
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