Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlin...

The Kuznetsov–Index of a modal logic is the least cardinal μ such that any consistent formula has a Kripke–model of size ≤ μ if it has a Kripke–model at all. The Kuznetsov–Spectrum is the set of all Kuznetsov–Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov–Index iω+ω. Futhermore, Chagrov has constructed an extension...

Abstract The nonlinear equation is obtained describing the dynamics of wave structures in dusty plasma above illuminated surface Moon case low frequencies and pancake-like shape packet direction along external magnetic field. This modified Zakharov – Kuznetsov equation. analytical formula for one-dimensional soliton solution derived. analysis stability was performed.

Abstract In this work, we investigate rogue wave (RW) clusters of different shapes, composed Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger equation (NLSE) with Kerr nonlinearity. We present three classes exact higher-order solutions on uniform background that are calculated using Darboux transformation (DT) scheme precisely chosen parameters. The first solution class is characteri...