mentioned in [1] as a model for the propagation of one-dimensional, unidirectional small amplitude long waves in nonlinear media. In GKdVB equation, μ, γ > 0 and α is a positive integer is considered, the independent variable x represents the medium of propagation, t is proportional to elapsed time, and u(x, t) is a velocity at the point x at time t. And If ν = 0, α = 1, the GKdVB equation (1) ...

With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of ...

We study the higher-order nonlinear dispersive equation ∂tu+ ∂ 2j+1 x u = ∑ 0≤j1+j2≤2j aj1,j2∂ j1 x u∂ j2 x u, x, t ∈ R. where u is a real(or complex-) valued function. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when a0,k 6= 0 for some k > j, in the sense that this equation cann...

We investigate $L^1\\to L^\\infty$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that evolution satisfies natural $t^{-\\frac{1}{2}}$ decay rate, which may be improved to $t^{-\\frac{1}{2} - \\gamma}$ any $0\\leq \\gamma<\\frac{3}{2}$ at cost of spatial weights. classify structure threshold obstructions as being composed space p...

Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on (1+4)-dimensional Myers-Perry black hole backgrounds with small angular momenta. The Myers-Perry space-times are generalizations of higher dimensional Kerr backgrounds where additional planes of rotation are ...

These notes were written as a guideline for a short talk; hence, the references and the statements of the theorems are often not given in full details. The point of these notes is to summarize the different directions that the study of dispersive equations has taken in the last ten years. I would like to mention here a few recent textbooks that treat different parts of this subject. They could ...

I will present recent results on the analytic description of the waves generated by a two-dimensional supersonic flow of a superfluid past a large slender obstacle [1]. If the speed of the oncoming flow is sufficiently high, the generated wave pattern in each half-plane generally represents a combination of two steady oblique dispersive shock waves (DSWs) having contrasting asymptotic propertie...

In this Letter, we study (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation by using the new generalized transformation in Homogeneous Balance Method (HBM). As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.  2002 Elsevi...

Classical relativistic field theory is used as a basis for a general discussion of the problem of splitting up the total energy-momentum tensor ofa system into contributions from its component subsystems. Both the Minkowski and Abraham forms (including electrostriction) arise naturally in alternative split-up procedures applied to a nondispersive dielectric fluid. The case of an electromagnetic...