Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation

Guan, Xue; Liu, Wenjun; Zhou, Qin; Biswas, Anjan

doi:10.1007/s11071-019-05275-0

Cited by 115 publications

(32 citation statements)

References 43 publications

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“…Finding the exact solutions for NLEE is an essential task as NLEE describes numerous phenomenon in nonlinear dynamics, engineering, optical fibre, plasma physics, fluid mechanics, natural sciences, etc. A large number of researchers and mathematicians have developed various effective techniques for computing exact solutions of NLPDEs (nonlinear partial differential equations), for instance, tanh function method [1], Hirota's bilinear method [2,3], the Jacobi elliptic function expansion method [4], Kudryashov method [5], the G ′ G -expansion method [6], Darboux transformation method [7], the Backlund transformation method [8], the inverse scattering method [9], Lie-symmetry analysis [10], multiple exp-function method, and many others. Among these techniques, GERF method [11][12][13][14] is very effective, robust and straightforward approach for finding the abundant exact soliton-form solutions of various NLPDEs.…”

Section: Introductionmentioning

confidence: 99%

A Study of (2+1)-Dimensional Konopelchenko-Dubrovsky (KD) System: Closed-Form Solutions, Solitary Waves, Bifurcation Analysis and Quasi-Periodic Solution

Kumar

Mann

Kharbanda

2022

Preprint

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Nonlinear evolution equations (NLEEs) are extensively used to establish the elementary propositions of natural circumstances. In this work, we study the Konopelchenko-Dubrovsky (KD) equation which depicts non-linear waves in mathematical physics with weak dispersion. The considered model is investigated using the combination of generalized exponential rational function (GERF) method and dynamical system method. The GERF method is utilized to generate closedform invariant solutions to the (2+1)-dimensional KD model in terms of trigonometric, hyperbolic, and exponential forms with the assistance of symbolic computations. Moreover, three-dimensional graphics are displayed to depict the behavior of obtained solitary wave solutions. The model is observed to have single and multiple soliton profiles, kink-wave profiles, and periodic oscillating nonlinear waves. These generated solutions have never been published in the literature. All the newly generated soliton solutions are checked by putting them back into the associated system with the soft computation via Wolfram Mathematica. Moreover, the system is converted into a planer dynamical system using a certain transformation and the analysis of bifurcation is examined. Furthermore, the quasi-periodic solution is investigated numerically for the perturbed system by inserting definite periodic forces into the considered model. With regard to the parameter of the perturbed model, two-dimensional and three-dimensional phase portraits are plotted.

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Section: Introductionmentioning

confidence: 99%

A Study of (2+1)-Dimensional Konopelchenko-Dubrovsky (KD) System: Closed-Form Solutions, Solitary Waves, Bifurcation Analysis and Quasi-Periodic Solution

Kumar

Mann

Kharbanda

2022

Preprint

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“…Many academics and mathematicians have worked hard over the last few decades to find explicit solutions to NPDEs. For this aim, many analytical methods have been created to obtain such exact solutions like sin-Gordon expansion method [11][12][13][14], the (1/G ) −expansion method [15][16][17], the simplified Hirota's method [18][19][20], the Backlund transformation method [21,22], and symbolic computational method [23]. The (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) reads [24][25][26]…”

Section: Introductionmentioning

confidence: 99%

New wave behaviors of the (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

Şener

2021

Journal of Mathematical Sciences and Modelling

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In this study, the (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation that indicated the propagation of nonlinear dispersive waves in inhomogeneous media is given for consideration. The generalized exponential rational function method is used to seek some new exact solutions for the considered equation. The three-dimensional surfaces and twodimensional graphs of the obtained solutions are plotted by choosing the appropriate values of the involving free parameters.

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“…A large variety of these equations are utilized to describe important phenomena in different scientifi field like, plasma physics [1,2], condensed matter physics [3], convective fluid [5], optical fiber [6,7], solid state physics [8,9], hydrodynamic [10], water waves [11] and many other branches of engineering [12][13][14]. In past years, to fin the exact solutions of NLSEs many powerful technique have been developed such as, the inverse scattering transformation [15], the homotopy perturbation method [16,17], the Darboux transformation method [18,19], the Sine-Gordon expansion method [20], Bernoulli sub-equation method [21], the modifie auxiliary equation mapping method [22,23], the Riccati equation mapping method [4], the extended sinh-Gordon equation expansion method [24],the modify extended direct algebraic method [25].…”

Section: Introductionmentioning

confidence: 99%

A variety of exact solutions for fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain in the semi classical limit

Akhtar¹,

Tariq²,

Khater³

et al. 2021

Rev. Mex. Fís.

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This paper investigates exact voyaging (2 + 1) dimensional Heisenberg ferromagnetic spin chain solutions with conformable fractional derivatives, an important family of nonlinear equations from Schrödinger (NLSE) for the construction of hyperbolic, trigonometric and complex function solutions. The detailed rational sine-cosine system and rational sinh-cosh system were used to locate dim, special and periodic wave solutions successfully. These findings suggest that the proposed approaches may be useful to investigate a range of solutions inside a repository of applied sciences and engineering, with success, quality, and trust. In addition, graphical representations and physical expresses of such solutions are represented by a set of the required values of the parameters involved. The methods are essentially adequate and can be extended to different dynamic models that create the nonlinear processes in today’s research.

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Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation

Cited by 115 publications

References 43 publications

A Study of (2+1)-Dimensional Konopelchenko-Dubrovsky (KD) System: Closed-Form Solutions, Solitary Waves, Bifurcation Analysis and Quasi-Periodic Solution

A Study of (2+1)-Dimensional Konopelchenko-Dubrovsky (KD) System: Closed-Form Solutions, Solitary Waves, Bifurcation Analysis and Quasi-Periodic Solution

New wave behaviors of the (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

A variety of exact solutions for fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain in the semi classical limit

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