2021
DOI: 10.21203/rs.3.rs-995301/v1
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Darboux Transformation, Exact Solutions and Conservation Laws for the Reverse Space-Time Fokas-Lenells Equation

Abstract: In this paper, we firstly deduce a reverse space-time Fokas-Lenells equation which can be derived from a rather simple but extremely important symmetry reduction of corresponding local equation. Next, the determinant representations of one-fold Darboux transformation and N-fold Darboux transformation are expressed in detail by special eigenfunctions of spectral problem. Depending on zero seed solution and nonzero seed solution, exact solutions, including bright soliton solutions, kink solutions, periodic solut… Show more

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Cited by 4 publications
(3 citation statements)
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“…After more than 100 years of development, a series of effective methods have emerged for the solving integrable systems, among which the well-known ones include Hirota bilinear method, inverse scattering transformation method, Darboux transformation (DT) method, etc. [1][2][3][4][5][6][7][8][9][10]. The emergence of these well-known methods has given an extremely powerful step forward in the development of nonlinear equations, and more equations with physical backgrounds are discovered and their numerical or analytical solutions are constructed, it is built a basis for whether solitons are destroyed after collisions occur.…”
Section: Modulation Instability Localized Wave Solutions Of the Modif...mentioning
confidence: 99%
“…After more than 100 years of development, a series of effective methods have emerged for the solving integrable systems, among which the well-known ones include Hirota bilinear method, inverse scattering transformation method, Darboux transformation (DT) method, etc. [1][2][3][4][5][6][7][8][9][10]. The emergence of these well-known methods has given an extremely powerful step forward in the development of nonlinear equations, and more equations with physical backgrounds are discovered and their numerical or analytical solutions are constructed, it is built a basis for whether solitons are destroyed after collisions occur.…”
Section: Modulation Instability Localized Wave Solutions Of the Modif...mentioning
confidence: 99%
“…Various methods have been proposed to explore nonlinear phenomena. For example, three-wave method [6,7], tanh method [8], Bäcklund transformation [9], Darboux transformation [10], Exp-function method [11], Hirota bilinear method [12], homogeneous balance method [13], the generally projective F-expansions [14], (G'/G)-expansion method [15], auxiliary equation method [16], Riccati equation method [17], simplest equation method [18,19], etc.…”
Section: Introductionmentioning
confidence: 99%
“…Various methods have been proposed to explore nonlinear phenomena. For example, three-wave method [6,7], tanh method [8], Bäcklund transformation [9], Darboux transformation [10], Exp-function method [11], Hirota bilinear method [12], homogeneous balance method [13], the generally projective F-expansions [14], (G'/G)-expansion method [15], auxiliary equation method [16], Riccati equation method [17], simplest equation method [18,19], etc.…”
Section: Introductionmentioning
confidence: 99%