In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...

We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by simple-wave type solutions hydrodynamic equations. In geometrical optics approximation, the motion packet obeys Hamilton equations with dispersion law playing role Hamiltonian. This Hamiltonian depends also on amplitude obeying Hopf-like equation for simple wave. The co...

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...

The study of wave and its propagation on the water surface is among significant phenomena in designing quay, marine and water structures. Therefore, in order to design structures which are exposed to direct wave forces, it is necessary to study and simulate water surface height and the wave forces on the structures body in different boundary conditions. In this study, the propagation of static ...

We argue that two specific wave packet families—curvelets and wave atoms—provide powerful tools for representing linear systems of hyperbolic differential equations with smooth, time-independent coefficients. In both cases, we prove that the matrix representation of the Green’s function is • sparse in the sense that the matrix entries decay nearly exponentially fast (i.e., faster than any negat...

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies Abstract – By a generalized bidirectional decomposition method, we obtain new Super-luminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several of them being endowed with finite total energy. ...

This paper explores the properties of nonlinear wave equations. The proof for the existence and uniqueness of solutions to the 1+1 dimensional linear wave equation with smooth data is given. The D’Alembert formula is then presented in its full generality for the nonlinear equation. Important properties like the domain of dependence and propagation of information are discussed and motivated. The...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...