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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 ...
On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation
(Wiley, 2022-01)
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 ...
Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation
(Elsevier, 2022-12-25)
In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using ...
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 ...
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 ...
Lump solutions of the fractional Kadomtsev–Petviashvili equation
(Springer, 2024-01)
Of concern is the fractional Kadomtsev–Petviashvili (fKP) equation and its lump solution. As in the classical Kadomtsev–Petviashvili equation, the fKP equation comes in two versions: fKP-I (strong surface tension case) and ...
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