Results 51 to 60 of about 3,238 (183)
Complexity, 2019 We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are ...
Shou-Ting Chen, Wen-Xiu Ma
doaj +1 more source
Journal of Ocean Engineering and Science, 2023 The paper investigates the multiple rogue wave solutions associated with the generalized Hirota–Satsuma–Ito (HSI) equation and the newly proposed extended (3 + 1)-dimensional Jimbo–Miwa (JM) equation with the help of a symbolic computation technique.
Saima Arshed +4 more
doaj +1 more source
Fusion rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds
, 1997 We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota equation). The
Lipan, O., Wiegmann, P. B., Zabrodin, A.
core +1 more source
Journal of Mathematics, Volume 2026, Issue 1, 2026.To investigate the fractional coupled Wu‐Zhang system analytically, this paper uses a hybrid generalized Riccati−Bernoulli sub‐ODE scheme and Bäcklund transformation to find the exact kink, antikink, and bright‐kink soliton solutions. The dynamical properties of these solutions are discussed using Hamiltonian formulation, phase‐portrait analysis, and ...
M. Mossa Al-Sawalha +2 more
wiley +1 more source
Higher order Hirota bilinear forms
In this paper we study Hirota bilinear forms of the type $P(D) \{f\cdot f\}=0$. We prove that for $P(D)=D_x^mD_y^rD_t^n$ the equations have three-soliton solutions if only if two of nonzero $m,n,p$ are odd and the other one even. We explicitly derive the nonlinear partial differential equations corresponding to this form for $m+n+p=4$ and $m+n+p=6$. We
Gürses, Metin, Pekcan, Aslı
openaire +2 more sources
Journal of Mathematics, Volume 2026, Issue 1, 2026.The Hirota–Maccari (HM) system is a fundamental model in wave propagation that has been widely utilized to investigate complex nonlinear phenomena in nonlinear optics, optical communications, and mathematical physics. The HM system sheds light on critical insights into soliton dynamics, wave interactions, and other nonlinear effects.
Fei Li +4 more
wiley +1 more source
Bilinearization of Discrete Soliton Equations and Singularity Confinement
, 1996 Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement.
Grammaticos +14 more
core +1 more source
Linear Subspaces of Solutions Applied to Hirota Bilinear Equation
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
doaj
Heliyon, 2020 A bilinear form of the (2+1)-dimensional nonlinear Calogero–Bogoyavlenskii–Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter.
Harun-Or- Roshid +2 more
doaj +1 more source
Open Physics, 2022 In this work, a (2+1)-dimensional generalized Hirota–Satsuma–Ito equation realized to represent the propagation of unidirectional shallow water waves is investigated.
Zhang Yun-Xia, Xiao Li-Na
doaj +1 more source