Soliton solutions of some nonlinear evolution equations in shallow water theory

Javeed, Shumaila; İnç, Mustafa; Abbasi, Muhammad Awais; Mahmoud, Khaled H.; Zafar, Zain Ul Abadin; Razzaq, Sohail

doi:10.1016/j.rinp.2022.105546

Cited by 4 publications

(1 citation statement)

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“…Obtaining new analytical solutions for various models formed by NLPDE has wide application in nonlinear physics fields including fluid dynamics, fiber optics, plasma physics, and optics. Considering the rapid growth of symbolic computation systems, soliton solutions make it possible to analyze nonlinear physical phenomena; thus, examination of the soliton solutions for NLPDE has recently attracted the attention of researchers [1,2]. In the literature, there are diverse approaches applied by researchers to produce analytical solutions of NLPDE such as the first integral method [3,4], the extended Kudryashov technique [5], the Riccati Bernoulli sub-ODE scheme [6,7], the modified simple equation scheme [8], the extended rational sine-cosine and sinh-cosh method [9], the extended Poincare-Lighthill-Kuo method [10], the extended simplest equation method [11], traveling wave solution [12], the auxiliary ordinary differential equation method and the generalized Riccati method [13], the solitary wave solution technique with the…”

Section: Introductionmentioning

confidence: 99%

Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method

Secer,

Bayram,

Ozdemir

et al. 2024

Phys. Scr.

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In this manuscript, we take into account the nonlinear complex generalized Zakharov dynamicalsystem, which models the spread of the Langmuir waves in ionized plasma in a conformalsense. Fractional wave transformation is enforced to convert a nonlinear fractional systemto a nonlinear ordinary differential equation system. The new Kudryashov method, whichwas recently introduced and is an efficient method, is implemented in the presented equationin order to acquire analytical solutions. The required constraint conditions are offered toensure the validity of the obtained solutions. To analyze the physical interpretations of someof the produced solutions, we illustrate some graphical representations. We derive brightand singular solitons. Furthermore, 2D views of the behavior of soliton are represented toinvestigate the effect of the values of the parameters in the proposed model and the fractionalparameter. Also, the modulation instability of the model is investigated to ensure theobtained results are stable.

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