Homoclinic breaters, mulitwave, periodic cross-kink and periodic cross-rational solutions for improved perturbed nonlinear Schrödinger's with quadratic-cubic nonlinearity

Rizvi, Syed T. R.; Seadawy, Aly R.; Batool, Tahira; Ashraf, Muhammad

doi:10.1016/j.chaos.2022.112353

Cited by 16 publications

(5 citation statements)

References 42 publications

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“…In this section, we work on MSRs with double kinks which consist of two exponential functions. We consider [2]…”

Section: Msr With a Two-kink Solutionmentioning

confidence: 99%

“…A partial differential equation (PDE) depicts the relationships between several partial derivatives of a variety of multivariate functions. Physics and engineering are two mathematics-based sciences that frequently use PDEs [1][2][3][4]. The fundamentals of contemporary scientific logic are formed by them for several ideas, including heat, sound, diffusion, electrodynamics [5][6][7], electrostatics, elastic, hydrodynamics, and quantum mechanics [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

Self Cite

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We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots.

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“…In this section, we work on MSRs with double kinks which consist of two exponential functions. We consider [2]…”

Section: Msr With a Two-kink Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

Self Cite

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“…In order to produce periodic, rational function, dark singular combo, and dark soliton solutions for IPNLSE with the influence of Kerr law nonlinearity, the extended V-expansion technique was utilized in [28]. Rizvi et al studied the soliton solutions of the IPNLSE with quadratic-cubic law nonlinearity with the help of the symbolic computation and log transformation with the ansatz function approach in [33]. In [29], it was aimed to obtain different soliton types like parabolic, M-and S-shaped, singular, bright, periodic and anti-dark soliton solutions of IPNLSE utilizing Hirota bilinear and generalized extended auxiliary equation mapping architectonic approaches.…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

Esen,

Onder,

Secer

et al. 2024

Phys. Scr.

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This paper was organized to examine the analytical solutions of the improved perturbednonlinear Schr ̈odinger equation with parabolic law with non-local nonlinearity in the pres-ence of chromatic dispersion and spatio-temporal dispersion. This model mostly makes useof studying the propagation of optical pulses in fiber optic communication systems. Weperformed the Sinh-Gordon equation expansion method so that we produce the analyticalsolutions of the model under consideration. It was confirmed that the acquired solutionssatisfy the main model. Therefore, bright and dark soliton solutions were retrieved; besides,various 3D and 2D graphical illustrations of the solitons were demonstrated via appropriatevalues of the parameters. Furthermore, this manuscript focused on the parameters’ effecton the acquired solitons behavior.

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“…Nonlinear evolution equations (NLEEs) are significantly used to observe numerous physical phenomena that appear in mathematical physics, condensed matter physics, water surface gravity waves, ion-acoustic waves in plasmas etc. [7,9,27,29,30,36]. The exact solutions for NLEEs play a vital role to study the dynamics of the evolution of native phenomena.…”

Section: Introductionmentioning

confidence: 99%

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

Batool

Seadawy

Rizvi

2023

NAMC

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In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions.

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Homoclinic breaters, mulitwave, periodic cross-kink and periodic cross-rational solutions for improved perturbed nonlinear Schrödinger's with quadratic-cubic nonlinearity

Cited by 16 publications

References 42 publications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

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