On the conformable nonlinear schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients

Rezazadeh, Hadi; Odabaşı, Meryem; Tariq, Kalim U.; Abazari, Reza; Başkonuş, Hacı Mehmet

doi:10.1016/j.cjph.2021.01.012

Cited by 58 publications

(8 citation statements)

References 47 publications

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“…It is used in many fields of physics like fluid mechanics, fundamental particle physics, biophysics. The NLSE is seen in non-linear optics, hydromagnetic and plasma waves and such [14][15][16][17][18][19][20] .…”

Section: Introductionmentioning

confidence: 99%

On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

TAZGAN

Çelık

Yel

2023

Gazi University Journal of Science

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In this work, we use two different analytic schemes which are the Sine-Gordon expansion technique and the modified exp -expansion function technique to construct novel exact solutions of the non-linear Schrödinger equation, describing gravity waves in infinite deep water, in the sense of conformable derivative. After getting various travelling wave solutions, we plot 3D, 2D and contour surfaces to present behaviours obtained exact solutions.

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Section: Introductionmentioning

confidence: 99%

On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

TAZGAN

Çelık

Yel

2023

Gazi University Journal of Science

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“…Its significance lies in its ability to satisfy the product formula, quotient formula, and simplified chain rule formula. Nowadays, the conformal fractional derivative definition has more adoption [8] than the other ones which have no similarity with the classical derivative. Also, finding exact solutions of fractional partial differential equations (FPDEs) is a difficult task to deal with the older definitions of fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques

Gupta

Yadav

2023

Phys. Scr.

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The current work uses a (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar (KMN) modelto investigate optical soliton transmission across an optical fiber that maintains polarization. Three constructivetechniques, namely, the extended power series solution, the new generalized method, and the extendedsinh-Gordon expansion method are utilized to find the exact soliton solutions of this model. The invariantanalysis has been performed on the (2+1) dimensional time fractional KMN model by using the conformaltime fractional derivative. The symmetries obtained using conformal fractional derivative are compared withthe symmetries obtained for integer order KMN model because symmetries using Riemann Liouville fractionalderivative turned out to be trivial. The given system of fractional PDEs has been reduced by using differentialinvariants obtained from various linear combinations of vector fields associated with the infinitesimal generatorof symmetry transformations. These reduced systems of equations are then investigated for their exactsolutions

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“…Obtaining the exact solutions for nonlinear partial differential equations (PDEs) [1][2][3][4][5][6][7][8][9] have captured the attention of numerous researchers, where they have made use of several methodical approaches to achieve the analytic solutions for nonlinear PDEs as multiple solitons, breather, lump solution, kink solitary wave, rogue wave, and others. In recent years, a wide range of techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been established to understand the different aspects of these analytic solutions such as the Hirota bilinear method, Darboux transformation, simplified Hirota method, Bäcklund transformation, Lie symmetry analysis, Pfaffian technique, Inverse scattering method, and several other methods.…”

Section: Introductionmentioning

confidence: 99%

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

2022

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This research aims to investigate a generalized fifth-order nonlinear partial differential equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to study the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasma physics and other nonlinear sciences. The Painlev\'e analysis is used to determine the integrability of the equation, and the simplified Hirota technique is applied to construct multiple soliton solutions with an investigation of the dispersion relation and phase shift of the equation. We utilize a linear combination approach to construct a system of equations to obtain a general logarithmic transformation for dependent variable. We generate one-soliton, two-soliton, and three-soliton wave solutions using the simplified Hirota method and showcase the dynamics of these solutions graphically through interaction between one, two, and three solitons. We investigate the impact of the system's parameters on the solitons and periodic waves. The SK, Lax, and CDG equations have a wide range of applications in nonlinear dynamics, plasma physics, oceanography, soliton theory, fluid dynamics, and other sciences.

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On the conformable nonlinear schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients

Cited by 58 publications

References 47 publications

On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

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