Dynamics of localized wave solutions for the coupled Higgs field equation

Zhaqilao, Zhaqilao

doi:10.1007/s11071-020-05860-8

Cited by 13 publications

(5 citation statements)

References 35 publications

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“…57 Traveling wave solutions obtained in this study as a result of the application of the method are different from the literature. [42][43][44][45][46][47][48][49][50][51] In addition, the solutions presented with Equations (4.1) and (4.2) as a result of the specific definition of three parameters, namely, wave number, wave velocity, and frequency of the soliton, have been defined as general solutions. These solutions are more general than traveling wave solutions and differ from the literature.…”

Section: Resultsmentioning

confidence: 99%

“…43 In 2020, localized wave solutions for CHFE were created using the symbolic computation method by Zhaqilao. 44 Some of these solutions are called higher order rogue wave, the Ma breather, the Akhmediev breather, and the general breather. These solutions obtained by the Hirota binary linear form are correlated with each other, and it is emphasized that these solutions are important in particle physics.…”

Section: Introductionmentioning

confidence: 99%

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Traveling wave and general form solutions for the coupled Higgs system

Duran

Durur

Yokuş

2023

Math Methods in App Sciences

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In this study, the coupled Higgs system, which is a special case of the coupled Higgs field equation, which is effective in energy transport in the sub-particles of the atom, is discussed. With the help of the modified generalized exponential rational function method, which is an important instrument in obtaining traveling wave solutions, both the propagating wave solutions and general form solutions of coupled Higgs system are presented. These solutions are examined under some restrictive conditions as they are presented. It is argued that these solutions differ from the literature. The advantages and disadvantages of the method discussed in the conclusion and discussion section are discussed. In addition, the changes in the behavior of the traveling wave solution are discussed by giving physical meaning to some constants in the traveling wave solutions produced by the method. The effects on the traveling wave solution are analyzed for different values of wave number, wave velocity, and wave frequency, which have physically important meanings. In addition, the behaviors caused by these effects are supported with the help of simulation.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Traveling wave and general form solutions for the coupled Higgs system

Duran

Durur

Yokuş

2023

Math Methods in App Sciences

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“…Especially in mathematics and physics, researchers have made significant progress and obtained practical and valuable results. Abundant multi-soliton, M -lump, high-order breather and interaction solutions of NLEEs have been discussed, such as the Hirota–Satsuma–Ito equation (Zhao and He, 2021; Wang et al , 2021), KdV equation (Tan et al , 2019; Khuri, 2023), Kadomtsev–Petviashvili equation (Liu et al , 2019a, 2019b; Ma et al , 2021; Liu et al , 2022), coupled Higgs field equation (Zhaqilao, 2020), Calogero–Bogoyavlenskii–Konopelchenko–Schiff system (Han and Bao, 2022; Liu et al , 2021).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of breather waves, lump-kink solutions and interaction solutions for a (3+1)-dimensional generalized shallow water waves equation

Liu

2023

HFF

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Purpose This paper aims to study the breather, lump-kink and interaction solutions of a (3 + 1)-dimensional generalized shallow water waves (GSWW) equation, which describes water waves propagating in the ocean or is used for simulating weather. Design/methodology/approach Hirota bilinear form and the direct method are used to construct breather and lump-kink solutions of the GSWW equation. The “rational-cosh-cos-type” test function is applied to obtain three kinds of interaction solutions. Findings The fusion and fission of the interaction solutions between a lump wave and a 1-kink soliton of the GSWW equation are studied. The dynamics of three kinds of interaction solutions between lump, kink and periodic waves are discussed graphically. Originality/value This paper studies the breather, lump-kink and interaction solutions of the GSWW equation by using various approaches and provides some phenomena that have not been studied.

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“…Once we obtain the bilinear form of a NLPDE, rouge waves, lump solutions and diverse interaction solutions of the equation can be construct. Recently, N-solitons, M-lumps, high-order multi-breathers and interaction solutions of NLPDEs have been discussed, for example, the generalized (2+1)-dimensional Hirota-Satsuma-Ito equation (Zhao and He 2021;) the (2+1)-dimensional KdV equation (Tan et al 2019), the generalized variable-coefficient Kadomtsev-Petviashvili equation , the new extended Kadomtsev-Petviashvili equation , the coupled Higgs field equation (Zhaqilao 2020).…”

Section: Introductionmentioning

confidence: 99%

Novel dynamical behaviors of interaction solutions of the new (3+1)-dimensional integrable fourth-order nonlinear equation

Liu

Gao

2022

Preprint

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In this paper, the breather wave, rouge wave and interaction solutions of lumps and various solitary waves of the (3+1)-dimensional integrable fourth-order nonlinear equation are discussed. With the aid of the extended homoclinc test, the breather wave and rouge wave are gained. Subsequently, the interaction solutions between a lump wave and 1-kink soliton or 2-kink soliton are studied. In addition, four types of interaction solutions between lump, kink and periodic waves via a “rational-cosh-cos” type test function are constructed. Moreover, the dynamical characteristics of these obtained solutions are displayed using graphical analysis.

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Dynamics of localized wave solutions for the coupled Higgs field equation

Cited by 13 publications

References 35 publications

Traveling wave and general form solutions for the coupled Higgs system

Traveling wave and general form solutions for the coupled Higgs system

Dynamics of breather waves, lump-kink solutions and interaction solutions for a (3+1)-dimensional generalized shallow water waves equation

Novel dynamical behaviors of interaction solutions of the new (3+1)-dimensional integrable fourth-order nonlinear equation

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