Results 11 to 20 of about 3,238 (183)
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
doaj +3 more sources
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
openaire +5 more sources
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
openaire +4 more sources
The N-soliton solutions of the (2+1)-dimensional Hirota–Satsuma–Ito equation
Results in Physics, 2022 Through the Bäcklund transformation and Hirota bilinear form, the explicit solutions with localized structures for the (2+1)-dimensional Hirota–Satsuma–Ito equation are solved.
Zheng-Yi Ma, Jin-Xi Fei, Wei-Ping Cao
doaj +1 more source
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
doaj +1 more source
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
openaire +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
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
doaj +1 more source