Results 11 to 20 of about 27,126 (206)
Hints on the Hirota Bilinear Method
Acta Physica Polonica A, 2007 We discuss four stages of the Hirota bilinear method, for construction of soliton solutions to partial difierential equations: the proper substitution to express the equation in the bilinear variables (1), reduction of the excess degrees of freedom (2 ...
P. Goldstein
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Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method [PDF]
Theoretical and Mathematical Physics, 2006 We use the Hirota bilinear approach to consider physically relevant soliton solutions of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions, recently proposed for describing uniaxial waves in a cold collisionless plasma.
Jyh-Hao Lee, O. Pashaev
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Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method [PDF]
Nonlinear Dynamics, 2021 Based on the Hirota’s bilinear method, a more classic limit technique is perfected to obtain second-order smooth positons. Immediately afterwards, we propose an extremely ingenious limit approach in which higher-order smooth positons and breather ...
Zhao Zhang +3 more
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Vector shock soliton and the Hirota bilinear method [PDF]
Chaos, Solitons & Fractals, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
O. Pashaev, G. Tanoglu
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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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Results in Physics, 2023 This article discusses the behavior of specific dispersive waves to new (3+1)-dimensional Hirota bilinear equation (3D-HBE). The 3D-HBE is used as a governing equation for the propagation of waves in fluid dynamics.
U. Younas +5 more
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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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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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The Method of Hirota Bilinearization
, 2023 Bilinearization of a given nonlinear partial differential equation is very important not only to find soliton solutions but also to obtain other solutions such as the complexitons, positons, negatons, and lump solutions. In this work we study the bilinearization of nonlinear partial differential equations in $(2+1)$-dimensions.
Gürses, Metin, Pekcan, Aslı
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A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation
Open Physics, 2023 In this article, through the Hirota bilinear method and long wave limit method, based on the N-solitons, we construct the multiple lump solutions of the generalized (3+1)-dimensional Hirota–Satsuma–Ito equation.
Qi Feng-Hua +3 more
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