In this paper, the family of BBM equation with strong nonlinear dispersive B(m,n) equation is introduced. By using a simple and effective algebraic method ,some abundant exact solutions for this class of BBM equations are gotten and call its solutions with solitary patterns, solitary wave solution with singular point , smooth solitary wave solution , kink solution, antikink solution, floating s...

GLOSSARY dispersive: Characteristic of waves whose velocity of propagation depends on wave frequency. The shape of a dispersive wave packet changes as it moves along. eigenfunction: Functional shape of the horizontal and vertical components of wave motion versus depth in the ocean for a specific wave frequency. geometrical spreading: Process of amplitude reduction resulting from the progressive...

Surface wave method can be used to determine the properties of the component materials of a pavement structure. The measurements are made of the differences in the phase of a wave of the Rayleigh type, received at two points at known radial spacing from the source of the wave. Pavements for highways or airport runways are usually constructed of cement concrete. Such pavements are treated as a s...

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to ...

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) ...

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. The proofs...

Solitary-wave solutions of a nonlinearly dispersive evolution equation are considered. It is shown that these waves are unstable in a certain parameter range.

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. The proofs...

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539-541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solution...