Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations

2007 ◽  
Vol 368 (5) ◽  
pp. 383-390 ◽  
Author(s):  
A.A. Soliman
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Exact Traveling Wave Solution

scholarly journals EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740006 ◽  
Author(s):  
XIAO-JUN YANG ◽  
J. A. TENREIRO MACHADO ◽  
DUMITRU BALEANU
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Boussinesq Equation ◽  
Special Functions ◽  
Traveling Wave Solution ◽  
Nonlinear Pdes ◽  
Type Model ◽  
Fractal Domains ◽  
Fractal Domain ◽  
Exact Traveling Wave Solution

The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

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