Rich Soliton Structures for the Kraenkel-Manna-Merle (KMM) System in Ferromagnetic Materials

Li, Bang‐Qing; Ma, Yu‐Lan

doi:10.1007/s10948-017-4406-9

Cited by 55 publications

(7 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Various studies have been carried out by researchers recently to get solutions of the KMM system. For example Younas et Painleve method to KMM system [24,25]. Raza et al used the new auxiliary equation method and semi inverse technique for KMM system [26].…”

Section: Coefficientmentioning

confidence: 99%

Examination of Kraenkel-Manna-Merle System by Sine-Gordon Expansion Method

Demiray

BAYRAKCI

2022

Mugla Journal of Science and Technology

View full text Add to dashboard Cite

In this study, Kraenkel-Manna-Merle (KMM) system is discussed. Sine-Gordon expansion method (SGEM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to this system. Thus, some dark soliton, bright soliton and dark-bright soliton solutions of the KMM system have been obtained. In addition, by giving specific values to the achieved solutions, 2D and 3D graphics of the solutions were plotted by way of the Wolfram Mathematica 12 program.

show abstract

Section: Coefficientmentioning

confidence: 99%

Examination of Kraenkel-Manna-Merle System by Sine-Gordon Expansion Method

Demiray

BAYRAKCI

2022

Mugla Journal of Science and Technology

View full text Add to dashboard Cite

show abstract

“…With the development of technology, the transistor size is reduced to the nanometer scale. How to develop electronic components with higher density and faster storage speed is the practical reason why the HFSC equation is valued [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

New Traveling Wave Solutions for the (2 + 1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation

Han

Wen

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The principal objective of this article is to construct new exact soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets. Through using the complete discrimination system method, the traveling wave solutions are obtained. As a result, we get the traveling wave solutions of the Heisenberg ferromagnetic spin chain equation, which include rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions, inverse trigonometric function, logarithmic function. Some graphical representations of the problems and that of comparison are also provided.

show abstract

“…By applying the inverse scattering transformation method and the Wadati-Konno-Ichikawa scheme, the one-, two-, and three-loop and spike-like soliton solutions were constructed in [35]. A class of multiple-valued solitons were investigated by the generalized G/G ′ -expansion method [36]. The loop-like traveling wave solutions and loop-like soliton solutions were obtained via the auxiliary equation method [37,38].…”

Section: Introductionmentioning

confidence: 99%

Rogue wave, interaction solutions to the KMM system

Jin

Lin

2020

Journal of Magnetism and Magnetic Materials

View full text Add to dashboard Cite

In this paper, the consistent tanh expansion (CTE) method and the truncated Painlevé analysis are applied to the Kraenkel-Manna-Merle (KMM) system, which describes propagation of short wave in ferromagnets. Two series of analytic solutions of the original KMM system (free of damping effect) are obtained via the CTE method. The interaction solutions contain an arbitrary function, which provides a wide variety of choices to acquire new propagation structures. Particularly, the breather soliton, periodic oscillation soliton and multipole instanton are obtained. Furthermore, we obtain some exact solutions of the damped-KMM equation at the first time. On the other hand, a coupled equation containing quadri-linear form and trilinear form for the original KMM system is obtained by the truncated Painlevé analysis, and the rogue wave solution and interaction solutions between rogue wave and multi-soliton for the KMM system are discussed.

show abstract

Rich Soliton Structures for the Kraenkel-Manna-Merle (KMM) System in Ferromagnetic Materials

Cited by 55 publications

References 34 publications

Examination of Kraenkel-Manna-Merle System by Sine-Gordon Expansion Method

Examination of Kraenkel-Manna-Merle System by Sine-Gordon Expansion Method

New Traveling Wave Solutions for the (2 + 1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation

Rogue wave, interaction solutions to the KMM system

Contact Info

Product

Resources

About