New exact traveling wave solutions for the Klein–Gordon–Zakharov equations

Shang, Yadong; Huang, Yong; Yuan, Wenjun

doi:10.1016/j.camwa.2007.10.033

Cited by 44 publications

(35 citation statements)

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“…Due to their potential application in plasma physics, the nonlinear Klein-Gordon-Zakharov system has been paid attention by many researchers. some exact solutions for the Zakharov equations are obtained using different methods [4][5][6][7][8][9][14][15]. In the Ref.…”

Section: ( )mentioning

confidence: 99%

“…The rest of the paper is organized as follows: In Section 2, Klein-Gordon-Zakharov equations are generalized, and the three special types of Klein-Gordon-Zakharov equations with the positive fractional power terms are presented; In Section 3, the sub-ODEs with the positive fractional power terms are introduced, and the exact solutions are presented; In Section 4, the exact solutions of three new special types of the Klein-Gordon-Zakharov equations (5), (6) and (7) are derived with the aids of the sub-ODE with the positive fractional power terms, respectively; In Section 5, some conclusions are made briefly.…”

Section: ( )mentioning

confidence: 99%

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The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

Zhang

2016

Pramana - J Phys

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Abstract:In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact solutions of new special gKGZE, the subsidiary higher order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aids of the Sub-ODE, the exact solutions of three special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.

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Section: ( )mentioning

confidence: 99%

Section: ( )mentioning

confidence: 99%

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

Zhang

2016

Pramana - J Phys

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“…This system describes the interaction of the Langmuir wave and the ion acoustic wave in a high frequency plasma. More details are presented in [1] and the references therein. Recently, applying the trigonometric function series method, Zhang [2] studied the new exact travelling wave solutions of the Klein-Gordon equation…”

Section: Introductionmentioning

confidence: 99%

“…More details are presented in [1]. More recently, some exact solutions for the Zakharov equations are obtained by using different methods [3 -12].…”

Section: Introductionmentioning

confidence: 99%

“…More recently, some exact solutions for the Zakharov equations are obtained by using different methods [3 -12]. In [1], using the extended hyperbolic functions method presented in [13], Shang et al obtained the multiple exact explicit solutions of the KGZEs (1) and (2). These solutions include the solitary wave solutions of bell-type for u and n, the solitary wave solutions of kink-type for u and bell-type for n, the solitary wave solutions of a compound of the bell-type and the kink-type for u and n, the singular travelling wave solutions, the periodic travelling wave solutions of triangle functions type, and solitary wave solutions of rational function type.…”

Section: Introductionmentioning

confidence: 99%

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A Note on Exact Travelling Wave Solutions for the Klein–Gordon– Zakharov Equations

Zhang

Gan

et al. 2012

Zeitschrift Für Naturforschung A

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Analysis of fractional Klein–Gordon–Zakharov equations using efficient method

Benli

2020

Numer Methods Partial Differential Eq.

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In the present framework, the q-homotopy analysis transform method (q-HATM) we find the solution for the equation describing the interaction between Langmuir waves and the ion-acoustic waves in the plasma, called Klein-Gordon-Zakharov equations. The projected solution procedure is elegant unification of q-homotopy analysis technique with Laplace transform. The considered coupled nonlinear system analyzed with the different fractional-order to ensure the efficiency and applicability of the hired solution procedure. For distinct values of the parameters offered by the considered method and for different fractional-order, the physical behaviors of achieved solutions are captured in terms of surface and contour plots. To illustrate the accuracy and reliability of the considered method, we conducted the numerical simulation for different fractional order with the change in variables. The obtained results show that, the projected scheme is highly methodical, very effective, easy to implement and accurate to investigate the nature of fractional nonlinear coupled system exemplifying the real-world problems.

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New exact traveling wave solutions for the Klein–Gordon–Zakharov equations

Cited by 44 publications

References 20 publications

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

A Note on Exact Travelling Wave Solutions for the Klein–Gordon– Zakharov Equations

Analysis of fractional Klein–Gordon–Zakharov equations using efficient method

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