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The tanh method: I. Exact solutions of nonlinear evolution and wave equations
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
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
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
where := −∂2 t +∆ and u[0] := (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
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.