Results 11 to 20 of about 5,895,681 (193)
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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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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2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), 2023 The novel KdV model plays a significant part in the discovery of a variety of nonlinear ion acoustic wave and harmonic crystal phenomena. The new homoclinic method based on the Hirota bilinear form is used to create the bilinear form of the new KdV equation and uncover numerous new exact solu tions.
Yokus, Asif, Isah, Muhammad Abubakar
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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
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Some integrable maps and their Hirota bilinear forms [PDF]
Journal of Physics A: Mathematical and Theoretical, 2017 We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the ...
A N W Hone, T E Kouloukas, G R W Quispel
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Controllable forms for stabilising pole assignment design of generalised bilinear systems [PDF]
, 2011 Bilinear structures are able to represent nonlinear phenomena more accurately than linear models, and thereby help to extend the range of satisfactory control performance.
K.J. Burnham +8 more
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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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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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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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