The Bifurcations of Traveling Wave Solutions of the Kundu Equation

Yi, Yating; Liu, Zhengrong

doi:10.1155/2013/137475

Cited by 5 publications

(1 citation statement)

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“…Feng and Wang [8] discussed the algebraic curve method to obtain the explicit particular solitary solutions for the Kundu equation and the derivative Schrodinger equation. Yi and Liu [9] employed the bifurcation approach to explore the bifurcations of traveling wave solutions for the Kundu equation. Luo and Nadeem [10] established Mohand transform with HPM to obtain the numerical solution of FKEE and coupled FMTP.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme

Nadeem

Wahash²

2023

Journal of Function Spaces

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This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). Numerical results are derived in a rapid converge series form to improve the accuracy of the scheme greatly. Graphical representations and error distribution show that the two-scale approach is a very convenient tool.

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Section: Introductionmentioning

confidence: 99%