Linear Subspaces of Solutions Applied to Hirota Bilinear Equations [PDF]
Aceh International Journal of Science and Technology, 2012 - Linear subspace of solution is applied to Boussinesq and Kadomtseve-Petviashvili (KP) equations using Hirota bilinear transformation. A sufficient and necessary condition for the existence of linear subspaces of exponential travelling wave solutions to
M. Y. Adamu, E. Suleiman
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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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Hirota bilinear forms with 2-toroidal symmetry [PDF]
Physics Letters A, 1999 In this note, we compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type $A_l, D_l, E_l$.
Iohara, Kenji +2 more
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Prolongation structure of the KdV equation in the bilinear form of Hirota [PDF]
Journal of Physics A: Mathematical and General, 1990 Summary: The prolongation structure of the Korteweg-de Vries equation in the bilinear form of Hirota is determined, the resulting Lie algebra is realised and the Bäcklund transformation obtained from the prolongation structure is derived. The results are compared with those found by Wahlquist and Estabrook and by Hirota.
Roelofs, Marcel, Martini, Ruud
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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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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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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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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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Novel complex N-soliton and lump solutions for nonlocal breaking equation
Results in Physics, 2022 The Hirota bilinear method is applied to construct the new dynamics of complex N-soliton solutions for a nonlocal breaking equation. By using the auxiliary traveling wave function, the different-order soliton solutions, bifurcation solutions and lump ...
Shaofu Wang
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The soliton solutions for semidiscrete complex mKdV equation [PDF]
ITM Web of Conferences, 2020 The semidiscrete complex modified Korteweg–de Vries equation (semidiscrete cmKdV), which is the second member of the semidiscrete nonlinear Schrődinger hierarchy (Ablowitz–Ladik hierarchy), is solved using the Hirota bilinear formalism.
Babalic Corina N.
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