The Construction of the (2+1)-Dimensional Integrable Fokas-Lenells Equation and its Bilinear form by Hirota Method

Yıl 2018, Sayı: 4, 61 - 66, 04.12.2018

Meruyert Zhassybayeva Kuralay Yesmakhanova

Öz

Integrable nonlinear
differential equations are an important class of nonlinear wave equations that
admit exact soliton of the solutions. In order to construct such equations tend to apply the
method of mathematical physics, the inverse scattering problem method (ISPM),
which was discovered in 1967 by Gardner, Green, Kruskal, and Miura. This method
allows to solve more complicated problems.  One of these equations is the (1+1)-dimensional integrable Fokas-Lenells
equation, which was obtained by the bi-Hamiltonian method and appears as an
integrable generalization of the nonlinear Schrödinger equation. In this paper,
we have examined the (1+1)-dimensional Fokas-Lenells equation and in
order to find more interesting solutions we have constructed the
(2+1)-dimensional integrable Fokas-Lenells equation, whose integrability are
ensured by the existence of the Lax representation for it. In addition, using
the Hirota’s method a bilinear form of the equation is constructed which was
found by us, through which can be find its exact multisoliton solutions and
build their graphs.

Anahtar Kelimeler

Integrability, Lax representation, Fokas-Lenells equation, Hirota bilinear method, Soliton solutions

Kaynakça

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