Results 11 to 20 of about 314 (173)
Novel soliton solutions to a (2+1)-dimensional breaking soliton equation
Partial Differential Equations in Applied Mathematics, 2022 In this paper, a Hirota bilinear form is presented for a (2+1)-dimensional breaking soliton equation. Novel N-soliton solutions are constructed through an application of the Hiorta direct method.
Qi Chen, Xiao-ming Zhu, Jian-bing Zhang
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Bilinear Identities and Hirota’s Bilinear Forms for the (γ n , σ k )-KP Hierarchy [PDF]
Journal of Nonlinear Mathematical Physics, 2021 In this paper, we discuss how to construct the bilinear identities for the wave functions of the (γn, σk)-KP hierarchy and its Hirota’s bilinear forms. First, based on the corresponding squared eigenfunction symmetry of the KP hierarchy, we prove that the wave functions of the (γn, σk)-KP hierarchy are equal to the bilinear identities given in Sec.3 by
Yehui Huang +4 more
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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
Ye, Yichao +3 more
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Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation
Advances in Mathematical Physics, 2023 In this work, a (2 + 1)-dimensional Ito equation is investigated, which represents the generalization of the bilinear KdV equation. Abundant double-periodic soliton solutions to the (2 + 1)-dimensional Ito equation are presented by the Hirota bilinear ...
Wen-Hui Zhu +4 more
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Analytical Treatment of the Generalized Hirota-Satsuma-Ito Equation Arising in Shallow Water Wave
Advances in Mathematical Physics, 2021 In the current study, an analytical treatment is studied starting from the 2+1-dimensional generalized Hirota-Satsuma-Ito (HSI) equation. Based on the equation, we first establish the evolution equation and obtain rational function solutions by means of ...
Fan Yong-Yan +4 more
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Lump solutions to nonlinear partial differential equations via Hirota bilinear forms [PDF]
Journal of Differential Equations, 2018 Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A
Wen-Xiu Ma, Yuan Zhou
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Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation
Open Physics, 2021 The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field.
Seadawy Aly R. +4 more
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Linear Subspaces of Solutions Applied to Hirota Bilinear Equations
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 form of the regularized long wave equation and its multi-soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 We consider utmost significant model, namely, the regularized long-wave equation involving dispersion and weedy nonlinearity effects that arises in the nonlinear dynamics of phonon packets in crystals, shallow water, plasma and ion acoustic waves.
Mohammad Mobarak Hossain +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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