This paper is an introductory review of the problem of front propagation into unstable states.
Our presentation is centered around the concept of the asymptotic linear spreading velocity …

An extended tanh-function method is proposed for constructing multiple travelling wave
solutions of nonlinear partial differential equations (PDEs) in a unified way. The key idea of …

A systemized version of the tanh method is used to solve particular evolution and wave
equations. If one deals with conservative systems, one seeks travelling wave solutions in the …

The tanh-function method for finding explicit travelling solitary wave solutions to non-linear
evolution equations is described. The method is usually extremely tedious to use by hand …

Das dynamische Verhalten von DNA-Molekülen wirklich zu verstehen, gehört heute zu den
großen Herausforderungen der Grundlagenforschung in der Biochemie und …

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic
method is described to construct several kinds of exact travelling wave solutions for some …

Based on an extended tanh-function method, a general method is suggested to obtain
multiple travelling wave solutions for nonlinear partial differential equations (PDEs). The …

This monograph has grown out of research we started in 1987, although the foun dations
were laid in the 1970's when both of us were working on our doctoral theses, trying to …

Many solitary wave solutions of nonlinear partial differential equations can be written as a
polynomial in two elementary functions which satisfy a projective (hence linearizable) …

Generalized forms of the KdV, the nonlinear heat conduction, and Burgers–Fisher equations
are investigated. The analysis rests mainly on the standard tanh method. The focus is on the …