In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...

In this paper, we derive exact traveling wave solutions of the (2+1)-dimensional Nizhnik-NovikovVeselov (NNV) system by a presented method. The method appears to be efficient in seeking exact solutions of nonlinear equations. Key–Words: (G ′ G )-expansion method, Travelling wave solutions, (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) system, nonlinear equation, exact solution, evolution equa...

A particular dispersive generalization of long water wave equation in 1 + 1 dimensions, which is important in the study of matrix models without scaling limit, known as two–Boson (TB) equation, as well as the associated hierarchy has been derived from the zero curvature condition on the gauge group SL(2, R) ⊗ U(1). The supersymmetric extension of the two–Boson (sTB) hierarchy has similarly been...

This work aims at introducing some energy operators linked to the Teager-Kaiser energy operator and expands it from time to space in the real domain. We then show the decomposition of the functions of space and time differentiable at least twice in R using those energy operators. The second part of the work focuses on using the energy operators to redefine the general wave equation. The method ...

We prove dispersive estimates at low frequency in dimensions n ≥ 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance. This class includes potentials V ∈ L∞(R) satisfying V (x) = O ( 〈x〉−(n+1)/2−ǫ ) , ǫ > 0.

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...

In this work, we prove a comparison result for general class of nonlinear dispersive unidirectional wave equations. The nature one-dimensional waves occurs because convolution integral in space. For two specific choices the kernel function, Benjamin–Bona–Mahony equation and Rosenau that are particularly suitable to model water elastic waves, respectively, members class. We first an energy estim...

We consider the 2-dimensional quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation with large initial data. We also show the strong convergence result as the amplitude parameter goes to ∞. Both results rely on the Strichar...