Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

Exact Solutions of the Nonlinear Generalized Shallow Water Wave Equation

Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.

Renormalized Solutions of a Nonlinear Parabolic Equation with Double Degeneracy

with p ≥ 2 and b(s) ≥ 0 appropriately smooth. The equation (1.1) presents two kinds of degeneracy, since it is degenerate not only at points where b(u) = 0 but also at points where ∂ ∂x B(u) = 0 if p > 2. Using the method depending on the properties of convex functions, Kalashnikov [10] established the existence of continuous solutions of the Cauchy problem of the equation (1.1) with f ≡ 0 unde...

Generalized Nonlinear Equation and Solutions for Fluid Contour Deformations

We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a finite-difference expression, with a general solution that is a power series expansion with coefficients satisfying a nonlinear recursion relation. In the limit of ...