Khokhlov–Zabolotskaya–Kuznetsov equation (φt + φφx − αφxx)x − 1/2(φyy + φzz) = 0 and its solutions are analyzed. A series of complete exact analytical solutions related to the one-dimensional and vectorial inhomogeneous Burgers equation are presented. A concrete example which corresponds to a special form of the inhomogeneous term is analyzed. Reduction to the traveling wave solution is conside...

In this paper, the Laplace Decomposition Method (LDM) employed to obtain approximate analytical solutions of the Klein-Gordon equation. The results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme.

An exact solution of a two-dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem, the wetting transition remains second order and occurs at a lower temperature than that of the planar system. A comparison with numerical studies and other analytical approaches is made.

We discuss two methods of an exact stochastic representation of the non-Markovian quantum dynamics of open systems. The first method employs a pair of stochastic product vectors in the total system's state space, while the second method uses a pair of state vectors in the open system's state space and a random operator acting on the state space of the environment. Both techniques lead to an exa...

The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...

The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...

We present the exact solution to the non linear Monge differential equation λ(x, t)λx(x, t) = λt(x, t). It is widely accepted that the Monge equation is equivalent to the ODE .. X= 0 of free motion for particular conditions. Furthermore, the Monge Type equations are connected withX = F ( . X, X; t), which can be integrated with quadratures [1]. Other asymptotic solutions are discussed, see e.g....

We study two specific features of onsite breathers in Nonlinear Schrödinger systems on d-dimensional cubic lattices with arbitrary power nonlinearity (i.e., arbitrary nonlinear exponent, n): their wavefunctions and energies close to the anti-continuum limit – small hopping limit – and their excitation thresholds. Exact results are systematically compared to the predictions of the so-called expo...