Complex dynamics of perturbed solitary waves in a nonlinear saturable medium: A Melnikov approach

Kudryashov, Nikolay A.; Лаврова, С. Ф.

doi:10.1016/j.ijleo.2022.169454

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…, and then accepts p = 0, equation (21) turns into the new Kudryashov form [23,49]. Unify equation (20,21) with equation (12) considering equation (21,22) and gather the coefficients of the terms K l , then equate the coefficients to zero, we get an algebraic system. Later, solving the system, we derive soliton sets.…”

Section: The Kudryashov Auxiliary Equation Approachmentioning

confidence: 99%

“…Plugging equations (23), (21) into equation (10), after some algebraic adjustments we acquire the following system:…”

Section: Implementation Kaem To Bme-aclawmentioning

confidence: 99%

“…Furthermore, analytical and numerical schemes enlarging incessantly in the literature have crucial in examining soliton solutions of diverse NLSEs. Researchers have evolved diverse analytical and numerical approaches to acquire different soliton forms Such as, the new Kudryashovʼs scheme [10], the enhanced Kudryashovʼs approach [11,12], the improved extended Tanh-function technique [13], the extended trial function scheme [14], the unified Riccati equation expansion aprroach [15][16][17][18][19], the auxiliary equation technique [20], the Melnikov method [21], the generalized Kudryashov technique [22], the Kudryashov method [23], the enhanced modified extended tanh expansion approach [24][25][26][27], the Sardar sub-equation scheme [28][29][30][31], the Painlevé test approach [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion

Özdemir

2023

Phys. Scr.

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For the first time, the optical soliton solutions of the $(1+1)$-dimensional Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion are intended to be analyzed in detail. To attain this purpose, the new Kudryashov and the Kudryashov auxiliary equation technique are successfully implemented. Moreover, the impacts of model parameters on the soliton dynamics are scrutinized. The complex wave transformation is utilized to get the nonlinear ordinary differential equation form and to generate soliton solutions, the presented methods are performed. Finally, various graphical illustrations were derived and detailed comments were added on the solution results. The new Kudryashov approach and the Kudryashov auxiliary equation technique have been successfully performed and soliton solutions obtained. W-shape soliton was acquired with the new Kudryashov approach and the bright soliton was acquired with the Kudryashov auxiliary equation technique. Furthermore, diverse graphic descriptions that the resulting soliton solutions are obtained, and 2D graphs are presented and commented on. Since the Biswas-Milovic equation, which is the subject of much research, has an important role in nonlinear optics, different forms of the Biswas-Milovic equation are developed in the literature. The model in the presence of spatio-temporal dispersion was presented and scrutinized for the first time.

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