scholarly journals Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions

2021 ◽  
pp. 125272
Author(s):  
W.M. Schouten-Straatman ◽  
H.J. Hupkes
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Fully Discrete ◽  
Wave Solutions ◽  
Infinite Range Interactions ◽  
Infinite Range

scholarly journals Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Gravity Waves ◽  
Numerical Scheme ◽  
Water Regime ◽  
Approximate Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Fully Discrete ◽  
Two Fluids ◽  
Wave Solutions ◽  
Numerical Solver

We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. The accuracy of the numerical solver is checked using some exact travelling wave solutions of the system.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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