We consider the Klein–Gordon equation associated with the Laplace– Beltrami operator ∆ on real hyperbolic spaces of dimension n≥2; as ∆ has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well–posedness results for the c...

By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional Bogoyavlenskii equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional Bogoyavlenskii equation are successfully obtained. The computation for the method appears to be easier and faster by general mathematical software.

In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota’s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented. Keywords—three-wave method; (3+1)-dimensional Soliton equation; Hirota’s bilinear form.

We investigate time domain based electromagnetic inverse problems. This is done in the context of general polarization models (which include the familiar Debye and Lorentz models as special cases) for dielectric materials. A one-dimensional model based on time-windowed pulsed inputs is formulated and well-posedness results are given for the simulation problem. Numerical investigations of proble...

A modified mapping method is used to obtain variable separation solutions with two arbitrary functions of the (2+1)-dimensional modified dispersive water-wave system. Based on the variable separation solution and by selecting appropriate functions, we discuss interaction behaviours among special anti-solitons constructed by multi-valued functions. The analysis results exhibit that the interacti...

Solitons and chaos are two most important notions of nonlinear science [1]. They are widely applied in many natural sciences [2 – 5] such as chemistry, biology, mathematics, communication, and particularly in almost all branches of physics like fluid dynamics, plasma physics, field theory, optics, and condensed matter physics [6 – 8]. Usually, these two features are treated independently since ...

By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional soliton equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional soliton equation are successfully obtained. The computation for the method appears to be easier and faster by general mathematical software.

On the basis of the continuity equation and the Bernoulli equation in the steady form, a differential equation is developed to evaluate the successive water levels within compartments of an upright perforated wave absorber. Then the initial and boundary conditions are introduced and the differential equation is solved as an initial value problem. Finally the reflection coefficient from the wave...

We study nonlinear systems of hyperbolic PDE’s in Rd , the hyperbolicity is understood in a wider sense, namely multiple roots of the characteristic equation are allowed and dispersive equations are permitted. They describe wave propagation in dispersive nonlinear media such as, for example, electromagnetic waves in nonlinear photonic crystals. The initial data is assumed to be a finite sum of ...