The time fractional <i>D</i>(<i>m,n</i>) system: invariant analysis, explicit solution, conservation laws and optical soliton

Kumari, Pinki; Gupta, Rajesh Kumar; Kumar, Sachin

doi:10.1080/17455030.2020.1821122

Cited by 4 publications

(1 citation statement)

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“…To simplify the equation, symmetry analysis is performed for the KMN model in this article and the symmetries are used to reduce the model into the system of partial differential equations or ordinary differential equations. These reduced systems are then examined for exact solutions using various methods such as the new generalized method [48], the extended sinh-Gordon expansion method [49], and the explicit power series solution method [50].…”

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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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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Studies on a Three-Field Lattice System: N-Fold Darboux Transformation, Conservation Laws and Analytic Solutions

Shen

Tian

Yang

et al. 2023

Qual. Theory Dyn. Syst.

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Lie Symmetry and Exact Solutions of Conformable Time Fractional Schamel–Korteweg–De Vries Equation

Kumar,

Bansal

2024

Int. J. Appl. Comput. Math

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In this current study, a systematic investigation is performed to derive symmetry reductions of conformable time-fractional Schamel-KdV equation via the Lie symmetry method. Using the obtained Lie point symmetries of nonlinear FPDEs the symmetry reduction is generated and utilized for the reduction into an ordinary differential equation. Some solutions of the reduced fractional ODEs are found with two straightforward methods to consider its traveling wave solution and series solutions, respectively. The method consists of the solutions which are trigonometric, hyperbolic, and rational functions. Also, we presented some figures for the obtained explicit solutions.

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The time fractional D(m,n) system: invariant analysis, explicit solution, conservation laws and optical soliton

Cited by 4 publications

References 32 publications

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

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

Studies on a Three-Field Lattice System: N-Fold Darboux Transformation, Conservation Laws and Analytic Solutions

Lie Symmetry and Exact Solutions of Conformable Time Fractional Schamel–Korteweg–De Vries Equation

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