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.

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...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: q-waves Fourier–Laplace spectral theory Dispersion error Linearized rotating shallow water equation (LRSWE) Navier...

This paper is concerned with the global existence of dissipative solutions to the Camassa-Holm equation after wave breaking. By introducing a new set of independent and dependent variables, the evolution problem is rewritten as an O.D.E. in an L∞ space, containing a non-local source term which is discontinuous but has bounded directional variation along a suitable cone of directions. For a give...

in this research a three dimensional model is explained which simulate the oil spill behavior inseas. this model is the developed version of previous two-dimensional study of aghajanloo et al., 2013.because of three-dimensional nature of the oil dispersion/movement in water, this is a more realistic model of oil spill transport and fate in marine environment. the model is based on eulerian appr...

The Boussinesq equation has been of considerable interest in coastal and ocean engineering models for simulating surface water waves shallow seas harbors, tsunami wave propagation, overtopping, inundation, near-shore process. Consequently, the study deals with dynamics localized interaction solutions to a dimensionally reduced (2 + 1)-dimensional from N-soliton by Hirota’s bilinear method. inte...

A weakly-nonlinear analysis of the transient evolution of two-dimensional, standing waves in a rectangular basin is presented. The waves are resonated by periodic oscillation along an axis aligned with the wavenumber vector. The amplitude of oscillation is assumed to be small with respect to the basin dimensions. The effects of detuning, viscous damping, and cubic nonlinearity are all simultane...