The generalized fractional Benjamin–Bona–Mahony equation: Analytical and numerical results

Oruc, Goksu; Borluk, Handan; Muslu, Gülçin M.

doi:10.1016/j.physd.2020.132499

Cited by 13 publications

(21 citation statements)

References 15 publications

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“…Since we do not have the exact solutions for the general values of α we construct the solitary wave solutions of the fKdV equation numerically by using the Petviashvili iteration method. This method has been widely used for fractional equations [3,8,34,36]. We refer to [8] and [36] for details of the method while generating solitary wave solutions of the fKdV equation.…”

Section: Methodsmentioning

confidence: 99%

Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation

Borluk¹,

Bruell²,

Nilsson³

2021

Preprint

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Of concern are traveling wave solutions for the fractional Kadomtsev-Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev-Petviashvili (KP) equation, the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line solitary waves of fKP-I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line solitary waves for both fKP-I and fKP-II equations.

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Section: Methodsmentioning

confidence: 99%

Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation

Borluk¹,

Bruell²,

Nilsson³

2021

Preprint

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“…The method is widely used for the generation of traveling wave solutions. 25,[30][31][32][33] The iteration method for the periodic waves, a modification of standard Petviashvilli's algorithm, 25,31 is based on the following solution steps. First, we use the transformation…”

Section: Numerical Experimentsmentioning

confidence: 99%

On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

et al. 2021

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The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin-Bona-Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin-Bona-Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.

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“…In this section we propose a Petviashvili's iteration method for the numerical generation of periodic travelling wave solutions of the equation (1.1). The method is widely used for the generation of travelling wave solutions [12,13,22,26,28]. The iteration method for the periodic waves, a modification of standard Petviashvilli's algorithm [13,22], is based on the following solution steps.…”

Section: Numerical Experimentsmentioning

confidence: 99%

On the existence, uniqueness and stability of Periodic Waves for the fractional Benjamin-Bona-Mahony equation

Amaral¹,

Borluk²,

Muslu³

et al. 2021

Preprint

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The existence, uniqueness and spectral stability of periodic waves for the fractional Benjamin-Bona-Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We also propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin-Bona-Mahony equation, numerically.

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The generalized fractional Benjamin–Bona–Mahony equation: Analytical and numerical results

Cited by 13 publications

References 15 publications

Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation

Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation

On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

On the existence, uniqueness and stability of Periodic Waves for the fractional Benjamin-Bona-Mahony equation

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