An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for variants of the KdV–Burger and the K(n, n)–Burger equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exac...

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long wave and NizhnikVeselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known an...

The Darboux-dressing transformations are applied to the Lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both ‘bright’ and ‘dark’ soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of applicative interest, such as vector...

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

In this paper, we employ Nevanlinna’s value distribution theory to investigate the existence of meromorphic solutions of some algebraic differential equations. We obtain the representations of all meromorphic solutions of certain algebraic differential equations with constant coefficients and dominant term. Many results are the corollaries of our result, and we will give the complex method to f...

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 ...

In this article, we put a direct method to construct the rational solitary wave solutions for some nonlinear differential difference equations in mathematical physics which may be called the rational solitary wave difference method. We use the proposed method to construct the rational solitary exact solutions for some nonlinear differential difference equations via the lattice equation, the dis...

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 ...

The purpose of this paper is to show that certain sharp existence theorems for small amplitude nonlinear wave equations in the Minkowski space setting extend to the case of nonlinear Dirichlet-wave equations outside of obstacles. Our main result is that the obstacle version of the Strauss conjecture holds when the spatial dimension is equal to 4. The corresponding result for 4-dimensional Minko...