Soliton solutions of higher order dispersive cubic-quintic nonlinear Schrödinger equation and its applications

Sultan, Abdul Malik; Lu, Dianchen; Arshad, Muhammad; Rehman, Hamood Ur; Saleem, Muhammad Shoaib

doi:10.1016/j.cjph.2019.10.003

Cited by 35 publications

(6 citation statements)

References 39 publications

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“…The author in [36] constructed the analytical solutions of equation ( 6) by using the extended hyperbolic auxiliary equation method. Furthermore, some authors employed other techniques [12,35] to construct other wave solutions of higher order dispersive NLSE. The researcher in [45] adopted extended fan sub-equation technique to solve Eq.…”

Section: Results Analysis and Physical Interpretationmentioning

confidence: 99%

“…Moreover, the author in [36] constructed the analytical solutions of equation ( 6) by using the extendedjhyperbolic auxiliaryjequation method, and in [44] by using the subsidiaryjordinary differential equation method. Furthermore,jsome authorsjemployed otherjtechniques [12,35] to construct other wave solutions of higher order dispersive NLSE. For the complexity of Eq.…”

Section: Modified Exponential Rational Function Methodsmentioning

confidence: 99%

“…3 Proposed MERFM arising in nonlinear models 3.1 Higher order dispersive cubic-quintic NLSE Here, we consider the higherjorder dispersive NLSE [12,35,36,44] with both fourth-order dispersion effects and a quintic nonlinearity, telling the promulgation of optical pulse in a medium that displays a law of parabolic nonlinearity [37][38][39] in the form…”

Section: Modified Exponential Rational Function Methodsmentioning

confidence: 99%

“…As a general equation to describejthe propagation of wave packets in weaklyjnonlinear dispersive media, it appears in some branches of mathematics, physics, biology, etc. Includes: nonlinear optics, quantum mechanics, fluid physics, condensed matter physics, perturbation and phase transition theory and so on [12][13][14][15]. The NLSE has successfully explained many nonlinear phenomena; in particular, it is widely used to study the transmission and generation of solitons.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

Arshad

et al. 2022

Preprint

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In mathematical physics, the Schrödinger equations have very important applications in Quantum mechanics, transmission lines, and optical fibers. The higher-order nonlinear Schrödinger equations (NLSEs) having higher-order dispersion, nonlinearity and cubic-quintic terms illustrates the propagation in optical fibers of enormously short pulses. In this paper, we construct the wave solutions of the higher-order NLSE with cubic-quintic dispersion and generalized second-order spatiotemporal dispersive NLSE by using the modified exponential rational function method (MERFM). As results, narrative solitons solutions in different forms are obtained, such as bright-dark solitons, trigonometric function, hyperbolic function, rational function, exponential function, singular solutions etc. The constructed results are compared with existing solutions in the literature which confirm that some have not been found in previous studies and their structures play an important role to explain a lot of physical phenomenon. Moreover, the structures of the newly obtained solutions are described by given appropriate parameters, and some interesting and novel graphs are obtained, which are helpful to explain the complicated physical phenomena of these nonlinear models. As consequence show the predominant and effectiveness of MERFM, which is also suitable for solving similar mathematical and physical models in other fields.

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Section: Results Analysis and Physical Interpretationmentioning

confidence: 99%

Section: Modified Exponential Rational Function Methodsmentioning

confidence: 99%

Section: Modified Exponential Rational Function Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

Arshad

et al. 2022

Preprint

Self Cite

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“…The nonlinear equations play a vital role in modeling several phenomena arising in nonlinear sciences. From the last few decades, the physicists and mathematicians have revealed the capacity of the nonlinear differential equations representing nonlinear phenomena in different branches of applied sciences such as optics, optical fibers, birefringent fibers, plasma physics, elastic media, geology, human biology, fluid dynamics, ecology, engineering, fluid mechanics, applied mathematics, computer science, medicine, and many more [1–40]. The Cahn–Hilliard (CH) model [41–45] represents phase separation in the physical system such as alloy.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of convective–diffusive Cahn–Hilliard equation using extended direct algebraic method

Rehman

Ullah

Asjad

et al. 2020

Numerical Methods Partial

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In this paper, we apply the extended direct algebraic method to examine the soliton solutions as well as hyperbolic and trigonometric functions solutions of convective–diffusive Cahn–Hilliard equation describing the dynamic of separation phase for ternary iron alloys of (Fe ‐ Cr ‐ Mo) and (Fe ‐ X ‐ Cu). The outcomes reveal that our technique is very dynamic and straightforward. It is observed that the obtained exact solutions of this model are new in the literature. Moreover, various 2D and 3D graphs of the obtained solutions are presented to examine the physical understanding of the obtained results.

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Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Mirzazadeh,

Hashemi,

Akbulu

et al. 2024

Math Methods in App Sciences

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The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended ‐dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti‐cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended ‐dimensional nonlinear CKE with generalized anti‐cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1‐soliton, singular 1‐soliton, and bright 1‐soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended ‐dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields.

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Soliton solutions of higher order dispersive cubic-quintic nonlinear Schrödinger equation and its applications

Cited by 35 publications

References 39 publications

Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

Exact solutions of convective–diffusive Cahn–Hilliard equation using extended direct algebraic method

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

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