Browsing Natural and Mathematical Sciences by Subject "Solitary waves"
Now showing items 1-7 of 7
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The generalized fractional Benjamin–Bona–Mahony equation: Analytical and numerical results
(Elsevier, 2020-08)The generalized fractional Benjamin-Bona-Mahony (gfBBM) equation models the propagation of small amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. The equation involves two fractional terms ... -
Numerical computation of solitary wave solutions of the Rosenau equation
(Elsevier, 2020-11)We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave ... -
On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves
(Elsevier, 2022-09)Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev–Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies ... -
On the stability of solitary wave solutions for a generalized fractional Benjamin–Bona–Mahony equation
(IOP Publishing, 2022-03-03)In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well known smooth and positive solitary wave with ... -
Some remarks on the stability and instability properties of solitary waves for the double dispersion equation
(Estonian Academy of Sciences, 2015)In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(|u|p−1u)xx for p > 1, a ≥ b ... -
Transverse linear instability of solitary waves for coupled long-wave-short-wave interaction equations
(Elsevier, 2012-12)In this paper, we investigate the transverse linear instability of one-dimensional solitary wave solutions of the coupled system of two-dimensional long-wave–short-wave interaction equations. We show that the one-dimensional ... -
Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation
(Wiley, 2022-07)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 ...
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