Gaussian soliton solutions to a variety of nonlinear logarithmic Schrödinger equation

Wazwaz, Abdul‐Majid; El-Tantawy, S. A.

doi:10.1080/09205071.2016.1222312

Cited by 19 publications

(3 citation statements)

References 31 publications

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“…It also had been shown that the Gaussons can exist for any number of dimensions, and numerically are stable under collisions over a wide range of energies in one and two dimensional cases [4]. Therefore, the model is applied to different areas such as superfluidity, open quantum systems, quantum liquid mixtures, Bose-Einstein condensates, and so forth [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Biswas et al solved the Bousisinesq equation with first degree logarithmic nonlinearity [17]; Darvishi and Najafi gave the Gaussian waves for some logarithmic ZK equation [18]. In addition, Wazwaz et al studied several logarithmic nonlinear evolution equations and obtained Gaussian solitary waves solutions, such as the following log-KdV, log-KG, log-Boussinesq, log-BBM, log-BBM-KP, log-TRLW and so forth [20][21][22][23]:…”

Section: Introductionmentioning

confidence: 99%

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Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

Liu

2021

Commun. Theor. Phys.

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In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

Liu

2021

Commun. Theor. Phys.

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“…Finally, he obtained Gaussons for the (2+1)and the (3+1)-dimensional logarithmic-Boussinesq equations [7]. Besides, Wazwaz and El-Tantawy [8] investigated different forms of the nonlinear logarithmic Schrödinger equations.…”

Section: Introductionmentioning

confidence: 99%

Some extensions of Zakharov–Kuznetsov equations and their Gaussian solitary wave solutions

Darvishi¹,

Najafi²

2018

Phys. Scr.

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In this paper, first we introduce four novel extensions of Zakharov-Kuznetsov equations which are their logarithmic forms. Then, we investigate the new logarithmic equations for their Gaussian solitary waves. After that, we obtain Gaussian solitons for all models. We show that all logarithmic models are characterized by their Gaussian solitary waves. These extensions can conduct interested researchers to obtain logarithmic extensions for another equations. Besides, the presented Gaussian solitary waves can be useful both mathematically and physically.

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The Gaussian soliton in the Fermi–Pasta–Ulam chain

Liu

2021

Nonlinear Dyn

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Gaussian soliton solutions to a variety of nonlinear logarithmic Schrödinger equation

Cited by 19 publications

References 31 publications

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

Some extensions of Zakharov–Kuznetsov equations and their Gaussian solitary wave solutions

The Gaussian soliton in the Fermi–Pasta–Ulam chain

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