Studied here is the generalized Benjamin-Ono-Zakharov-Kuznetsov equation ut + upux + αH uxx + εuxyy = 0, (x, y) ∈ R2, t ∈ R+, in two space dimensions. Here, H is the Hilbert transform and sub-scripts denote partial differentiation. We classify when this equation possesses solitary-wave solutions in terms of the signs of the constants α and ε appearing in the dispersive terms and the strength of the non-linearity. Regularity and decay properties of these solitary wave are determined and their stability is studied.
In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.
AUTHOR KEYWORDS: Damped Boussinesq equation; Instability; Stationary solution INDEX KEYWORDS: Mathematical techniques; Plasma stability, Blow-up; Boussinesq equations; Global solutions; Stationary solutions; Suitable conditions, Initial value problems PUBLISHER: Kluwer Academic Publishers
In this work, we study the Cauchy problem of the sixth-order Boussinesq equation. We shall use the [k; Z]-multiplier norm method to get a bilinear estimate on nonlinear term, and the local well-posedness on H s(ℝ) is obtained for s > -3/4 .
AUTHOR KEYWORDS: Existence and uniqueness; stability; SVD method; the Tikhonov regularization method INDEX KEYWORDS: Efficient numerical method; Existence and uniqueness; Initial and boundary conditions; Inverse wave problems; Singular value decomposition method; SVD method; Tikhonov regularization; Tikhonov regularization method, Convergence of numerical methods; Numerical methods; Singular value decomposition, Inverse problems
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.
AUTHOR KEYWORDS: RGBO equation; Solitary waves; Stabilit
This paper investigates the existence and uniqueness of solutions to first-order nonlinear boundary value problems (BVPs) involving fuzzy differential equations and two-point boundary conditions. Some sufficient conditions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara differentiability.
AUTHOR KEYWORDS: Boundary value problems; Fuzzy differential equations; Fuzzy numbers
In this work, we study a two-dimensional version of the BBM equation. We prove that the Cauchy problem for this equation is globally well-posed in a natural space. We also show that the orbital stability of the solitary waves of the equation. Furthermore, we establish that if the solution of the Cauchy problem has a compact support for all times, then this solution vanishes identically.
Damghan University strives to be one of the top and outstanding universities in terms of scientific developments both theoretically and practically. Damghan University will have a transformative impact on society through innovation in education, research and entrepreneurship.