5. Hirota method | ScienceGate

In this paper a (1+1)-dimension equation of motion for φ4-theory is considered for the case of simultaneously taking into a account of the processes of dissipation and violation the Lorentz-invariance. A topological non-trivial solution of one-kink type for this equation is constructed in an analytical form. To this end, the modiﬁed direct Hirota method for solving the nonlinear partial derivatives equations was used. A modiﬁcation of the method lead to special conditions on the parameters of the model and the solution.

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Constructing a supersymmetric integrable system from the Hirota method in superspace

Nuclear Physics B ◽

10.1016/j.nuclphysb.2003.11.042 ◽

2004 ◽

Vol 681 (3) ◽

pp. 351-358 ◽

Cited By ~ 18

Author(s):

Debojit Sarma

Keyword(s):

Integrable System ◽

Hirota Method

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4. The τ-Function, the Hirota Method, the Painlevé Property and Bäcklund Transformations for the Korteweg—deVries Family of Soliton Equations

Solitons in Mathematics and Physics ◽

10.1137/1.9781611970227.ch4 ◽

1985 ◽

pp. 113-144

Keyword(s):

Hirota Method ◽

Bäcklund Transformations ◽

Soliton Equations ◽

Painlevé Property ◽

Backlund Transformations

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Comment on ‘Study of lump solutions to an extended Calogero-Bogoyavlenskii-Schiff equation involving three fourth-order terms’ (2020 Phys. Scr. 95 095207)

Physica Scripta ◽

10.1088/1402-4896/ac2fc0 ◽

2021 ◽

Vol 96 (12) ◽

pp. 127001

Author(s):

Xin-Yi Gao ◽

Yong-Jiang Guo ◽

Wen-Rui Shan

Keyword(s):

Fluid Dynamics ◽

Nonlinear Optics ◽

Plasma Physics ◽

Symbolic Computation ◽

Fourth Order ◽

Analytic Solutions ◽

Hirota Method ◽

Bäcklund Transformations ◽

Current Interest ◽

Lump Solutions

Abstract Of current interest, in nonlinear optics, fluid dynamics and plasma physics, the paper commented (i.e., Phys. Scr. 95, 095207, 2020) has investigated a (2+1)-dimensional extended Calogero-Bogoyavlenskii-Schiff system. Hereby, we make the issue raised in that paper more complete. Using the Hirota method and symbolic computation, we construct three sets of the bilinear auto-Bäcklund transformations for that system, along with some analytic solutions. As for the amplitude of the relevant wave in nonlinear optics, fluid dynamics or plasma physics, our results depend on the coefficients in that system.

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