Analytical Wave Solutions for Foam and KdV-Burgers Equations Using Extended Homogeneous Balance Method

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

The extended homogeneous balance method and exact solutions of the Maccari system

The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.

Complex-Valued Burgers and KdV-Burgers Equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mil...

Invariants of fast solutions of KdV-Burgers Equations

which is obtained from eq. (1) by replacing Uk with A 2 k and rescaling t, while the cyclic boundary condition case is discussed in Goodman & Lax [2] for even N . Moser notes the existence of dN/2e polynomials of Ak that are invariant and states that they are independent. They are the coefficients of the characteristic equation of an N + 1 by N + 1 zero-diagonal symmetric Jacobi matrix whose te...