No abstract available

[en] 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. (paper)

[en] We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogeneous term depends only on the variable space, the Fujita critical exponent and the second critical exponent in the sense of Lee and Ni are derived.

[en] In this article, for a time-fractional diffusion-wave equation ${\mathrm{\partial <!--\; ???\; -->}}_t^{\mathrm{\alpha <!--\; ??\; -->}}u(x,t)=-<!--\; ???\; -->Au(x,t)$, 0 < t < T with fractional order α ∈ (1, 2), we consider the backward problem in time: determine u(⋅, t), 0 < t < T by u(⋅, T) and ∂_t u(⋅, T). We prove that there exists a countably infinite set Λ ⊂ (0, ∞) with a unique accumulation point 0 such that the backward problem is well-posed for T ∉ Λ. (paper)

[en] The convergence of certain semidiscrete approximation schemes based on the velocity-stress formulation of the wave equation and spaces such as those introduced by Raviart and Thomas is discussed. The discussion also applies to similar schemes for the equations of elasticity

No abstract available

[en] In this note, the explicit form of the N soliton solutions for a class of the system of LS nonlinear wave interaction has been obtained by using Hirota's method. (author). 6 refs

[en] 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. (paper)

[en] In this paper, we use the generalized semiflow theory to study the longtime dynamical properties for a class of semilinear hyperbolic equations. The existence of global attractors is shown for the equations with no Lipschitz continuity assumption on their nonlinear terms. The results obtained here are generalizations of the related ones in Ball [Ball JM. Global attractors for damped semilinear wave equations. Discret Contin Dyn Syst 2004;10:31-52]

[en] The harmonic wave equation in inhomogeneous media is exactly split into coupled first-order equations with respect to a principal direction of propagation according to the Bremmer scheme. The resulting one-way wave equation is shown not to conserve energy flux for dimensions two and three against the general belief in one-way wave propagation or parabolic equation literature. Conservation of energy flux is only ensured in the high frequency limit. On the other hand, a simple invariant is found that may be seen as a generalization of the Snell law to arbitrary, non-stratified, media. Similarly, the reciprocity property is not fully ensured in general and the time-reversal symmetry is ensured for propagating fields. Besides, in the one-way wave equation, the additional term to the standard parabolic equation is shown to strengthen mode coupling. The analysis encompasses the evanescent waves