• Publications
• Influence
The tanh method: I. Exact solutions of nonlinear evolution and wave equations
• Mathematics
• 1 December 1996
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 form of a finite
The tanh method: II. Perturbation technique for conservative systems
• Physics
• 1 December 1996
With the aid of the tanh method, nonlinear wave equations are solved in a perturbative way. First, the KdVBurgers equation is investigated in the limit of weak dispersion. As a result, a general
Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method
• Mathematics
• 1 April 1986
The authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear
Shallow Water Waves and Solitary Waves
• W. Hereman
• Environmental Science
Encyclopedia of Complexity and Systems Science
• 25 August 2013
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely
Nonlinear Wave Equations
• Mathematics
• 26 March 2015
where := −∂2 t +∆ and u := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F
Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations
• Mathematics
J. Symb. Comput.
• 27 February 1997
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented and the code is tested on several well-known partial differential equations from soliton theory.