... independent functions and hence their coefficients must be zero. That implies: (Equation 12) and: (Equation 13) Exp-function method Mathematical physics Solitons Integrability Lie symmetry The theory of nonlinear waves is one of the most important areas of research Ocean...

... Allen‐Cahn equation Non‐periodic boundary conditions Different time‐stepping methods Chebyshev spectral method Fluid dynamics Mathematical physics Consider the initial‐boundary value problem of the form: Equation 1 where u indicates the phase state at each point in spaces...

... role in mathematical physics and engineering sciences. Design/methodology/approach In this paper, the authors apply the exp‐function method to construct exact solutions of nonlinear wave equations. Findings In total, four forms of the extended shallow water wave equation have been studied, from...